Shape and size of bovine rhodopsin: A small-angle X-ray scattering study of a rhodopsin-detergent complex

J. Mol. Biol. (1976) 105, 383407

Shape and Size of Bovine Rhodopsin: A Small-angle X-ray Scattering Study of a Rhodopsin-Detergent Complex CHRISTIAN SARDET~, ANNETTE TARDIEU AND VITTORIO LOZZATI

Centre de Gth%~que Mokkuluire du C.N.R.S. 91190 Gif-sur- Yvette, France (Received 18 December 1975) Rhodopsin is extracted from rod outer segments of retinas with dodecyldimethylamine oxide (DDAO), a non-ionie detergent. The rhodopsin-DDAO complex is characterized by binding experiments, gel filtration, sedimentation, densimetry ; its homogeneity, chemical composition, weight and partial specific volume are determined. The complex turns out to be a reasonably monodisperse association of one rhodopsin and 156 DDAO molecules. The rhodopsin-DDAO complex and the detergent micelles are studied by small-angle X-ray scattering techniques using a water/sucrose solvent of variable density. The experiments are performed on an absolute scale; mainly the value and curvature of the scattering curves at zero angle are exploited. The structure of the complex and of the micelles is shown to be independent of sucrose. Under these conditions the final result of the X-ray scattering study of each type of particle is the numerical value of a set of five parameters : molecular weight, volume and radius of gyration of the volume occupied by the particles, average electron density and second moment of the electron density fluctuations inside the particles. It is also shown that in the complex the centres of gravity of rhodopsin and of the detergent moiety are very near to each other. The analysis of these parameters leads to the determination of the size and shape of the detergent micelles and to an estimate of the size and shape of the volumes occupied by protein and by detergent in the complex. We find rhodopsin to be a very elongsted molecule (maximum diameter -95 A) which spans a flat detergent micelle. These results suggest that in the rod outer segment discs the rhodopsin molecules span the membranes, that the rhodopsin molecules of the two opposite membranes of each disc come near to each other and that a high fraction of the intra-disc space is occupied by rhodopsin.

1. Introduction Little is known about the structure of integral membrane proteins, besides the fact that some span the membrane and others have a hydrophobic tail embedded in the lipid bilayer (Singer, 1974 ; Bretscher, 1973 ; Strittmatter et al., 1972). A remarkable exception is bacteriorhodopsin whose structure was recently determined at 7 A resolution (Henderson & Unwin, 1975). One reason for the general lack of information about membrane proteins is the difficulty of dispersing them in solvents or of ordering them in crystalline lattices, since most morphological and structural techniques require either dilute solutions or crystals. A number of membrane proteins have, however, been purified and solubilized in the presence of detergents, and particles have been obtained which contain one or more protein molecules associated with t Present eddress: Station Zoologique, La Darse, 06230 Villefranche-sur-Mer, 383

Franoe.

384

C. SARDET,

A. TARDIEU

AND

V. LUZZATI

stoichiometric amounts of detergent (it can be noted that membrane proteins bind substantial amounts of detergents whereas soluble proteins do not; Helenius Q Simons, 19’75; Robinson & Tanford, 1975; Clarke, 1975; Osborne et al., 1974). These protein-detergent complexes display conspicuous electron density fluctuations due to the presence of hydrocarbons and proteins, and can thus be studied by smallangle X-ray (and neutron) scattering techniques using solvents of variable density. Recent developments of this technique and an application to human serum lipoproteins (Luzzati et al., 1976; Tardieu et al., 1976) show that in a system containing proteins and lipids the contribution of the polar moiety can be disentangled from that of the hydrocarbon chains and information gained about the shape and size of the two regions. We describe in this work a small-angle X-ray scattering study of a rhodopsindetergent complex. Rhodopsin is the major protein component of the membranes of rod outer segments. It contains a chromophore, ll-cis retinal, and an apoprotein, opsin; its molecular weight is 39,199 (Daemen et al., 1972). Rhodopsin can be extracted from the rod outer segments by several detergents and can be obtained free of lipids in the form of a complex containing one molecule of rhodopsin and a large number of molecules of detergent (Osborne et al., 1974). In this work we use dodecyldimethylamine oxide in its non-ionic form; this chemically homogeneous detergent has already been used to purify rhodopsin (Applebury et al., 1974; Ebrey, 1971). The biochemical part of our study deals with the characterization of the rhodopsin-DDAOt complex, namely the determination of its homogeneity, chemical composition, weight and partial specific volume. The X-ray scattering study is performed on the detergent micelles and on the protein-detergent complex, sucrose being used to raise the electron density of the solvent. Only this very smallangle region of the X-ray scattering curves is explored in most of this work, the experiments being carried out on an absolute scale. As a consequence the final result, of the X-ray study is a set of five parameters: the particle weight, the volume and radius of gyration of the volume occupied by the particle, the average electron density and the second moment of the electron density fluctuations inside the particle. The analysis of these parameters leads to the determination of the shape and size of the detergent micelles and to an estimate of the dimensions of the protein and detergent regions of the complex. We can anticipate that the rhodopsin molecules will turn out to be thin elongated objects, with maximum length of at least 90 & surrounded in their central part by the detergent molecules. The model we put forward can be described as a disk-like detergent micelle spanned by one molecule of rhodopsin. From the technical standpoint we may point out that the use of a position-sensitive detector (Gabriel & DuPont, 1972) is essential for the X-ray scattering experiments carried out in this work, and that the analysis of the X-ray data involves some novel theoretical aspects which are described below. 2. Techniques (a) Biochemical and physico-chemical

experiments

(i) Detergent

Dodecyldimethylamine oxide was synthesized from redistilled dodecylamine (Fluka), recrystallized and checked for purity as described (Applebury et al., 1974). [W]DDAO t Abbreviation

used: DDAO,

dodecyldimethylamine

oxide.

A RHODOPSIN-DETERGENT

COMPLEX

385

(24 mCi/mmol) was obtained from the C.E.A. Saclay, France. Detergent solutions were made in imidazole/HCl buffers (50 m&r), 1 m&r-dithiothreitol (pH 7.0) (Im buffer), in which the detergent is non-ionic, end above 0.5 mg/ml (critical micellar concentration); under these aonditions DDAO aggregates in micelles of 75 molecules (Herrmann, 1962). Ammonyx LO, a commercial version of DDAO with 30% tetradecylamine oxide, came from Onyx Chemical. (ii) Rhodopsin Rod outer segment membranes were prepared from retinas of the eyes of freshly slaughtered cows (Osborne et al., 1974). Rhodopsin was purified in Ammonyx LO and DDAO by a procedure inspired by Applebury et al. (1974). Freeze-dried rod outer segments obtained from a hundred retinas containing 20 to 30 mg of rhodopsin were dissolved in 10 ml Im buffer with 50 mg detergent/ml, stirred overnight at 4°C and centrifuged 20 min at 20,000 revs/min in an SS34 Sorvdl rotor to pellet undissolved opsin. The supernatant was deposited on a hydroxylapatite (HT Bio Rad) column (4 = 1.5 cm) packed to a minimum height of 20 cm and equilibrated overnight with at least 150 ml of Ammonyx LO (15 mg/ml) in Im buffer. A linear gradient (160 ml) was then applied from 5 to 150 muPi in Ammonyx LO (15 mg/ml)/Im buffer with a peristaltic pump to detach successively lipids and retinol, opsin and finally rhodopsin from the absorbent. The fractions containing rhodopsin (2 ml) were pooled and dialyzed overnight against, Ammonyx LO (2 mg/ml)/Im buffer to remove phosphate. (iii) Concentration of rhodopsin and binding of DDAO The dialyzed solution was deposited on a column (4 = 1.5 cm) containing just enough hydroxylapatite (3 to 4 cm) to absorb rhodopsin. Ammonyx LO was then exchanged for [14C]DDA0 by elution with 30 ml Im buffer containing 2 mg [14C]DDAO/ml. The column was monitored for a stable baseline of radioactivity corresponding to the elurtnt. Rhodopsin was eluted sharply with 150 mM-P, in the eluant. Fractions of O-4 ml were collected, absorbences were determined from 650 to 260 nm on a Gary 15 spectrophotometer, and 20-pl samples were taken of 811fractions for scintillation counting (Osborne et al., 1974). There was no notable quenohing of radioactivity. Binding of [14C]DDA0 to rhodopsin was calcul&ed from ((ctsjmin in rhodopsin fraction - average cts/min before and after rhodopsin frsctions)/(ooncentration of rhodopsin from absorbance at 500 nm)) on rhodopsin fractions with a 500 nm absorbance greater than 3 (E, molar extinction coefficient, 40,300 M-l and 2M, 39,100; Daemen et al., 1972). The experiments were also performed with solutions containing 50% sucrose. In order to estimate lipid phosphorus, baseline fractions and rhodopsin-containing fractions were dialyzed for 2 to 3 days against several changes of water containing detergent to remove inorganic phosphate; lipid phosphorus was then measured (Osborne et al., 1974). (iv) GeZchromatography Gel beads of 10% Agarose (Bio Rad 0.5 M) were equilibrated in a Sephadex column (4, 2.5 om) up to a height of 45 cm with Im buffer oont,aining 100 mM-N&l with or without DDAO (2 mg/ml) (exclusion volume (V,) and inclusion volume (Vi) were determined using blue dextran 2000 and [14C]glucose). Several proteins were chromatographed and measured in the fraction collected (1.5 ml vol. estimated by weighing) : 2 mg cat&se (Serve), detected by 400 nm absorption; 1 mg aldolese (Sigma) followed by its enzymatic activity (Blostein & Rutter, 1963); 5 mg bovine serum albumin (Sigma) detected by 280 nm absorption; 1 mg haemoglobin (Sigma) detected by 410 nm absorption; and rhodopsin (2 mg) chromatographed in the presence of DDAO in the elution buffer. Stokes’ radii given by Tanford et al. (1974) were used and the data were plotted according to Andrews (1970) (see Fig. 2). (v) Xedirnentation Sedimentation velocity experiments on purified rhodopsin in Im buffer containing 100 mM-N&l and DDAO (2 mg/ml as free detergent ooncn) were carried out in a Spinco model E ultracentrifuge at 20°C using an AnH rotor equipped with a double-sector cell.

C. SARDET,

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A. TARDIEU

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V. LUZZATI

Absorbances of the solutions were recorded at 500 nm on a photographic plate, at 32-min intervals. No bleaching was observed during the experiment (see Fig. 3). (vi) Densities

and partial

specific

volumes

Densities were measured et 21°C with an Anton Paar precision densimeter and partial specmc volumes were calculated from precise concentration and density measurements (Kratky et al., 1973). (vii)

Preparation

of samples for small-angle X-ray

Rhodopsin fractions binding measurements

scattering

(8 to 9 mg/ml), eluted from an hydroxylapatite were made, were dialyzed 24 h against eluant

column Im buffer

on which (2 mg/ml

DDAO, 50% or no sucrose present), to which 100 mu-NaCl was added, and binding was measured again. Samples of different sucrose concentration were made by mixing small volumes (10 and 100 ~1) with Pederson micropipettes in small cellulose acetate tubes of 2 basic solutions containing 0% sucrose/cold of the rhodopsin solutions DDAO radioactivity.

DDAO

and 50% sucrose/[14C]DDA0,

or DDAO

(b) Small-angle The X-ray

camera

background

X-ray scattering

and the experimental

respectively.

The density

could thus be checked, from the [r4C]-

experiments

procedure

are described elsewhere (Tardieu et al., 1976). Calibrated nickel filters are used to attenuate the incident beam and make its intensity commensurable with the scattered intensity (Luzzati et aE., 1963). The beam stop itself is a nickel foil approx. 0.3 mm thick which allows us to measure the energy of the incident beam integrated over the time of exposure. The sample is contained in quartz capillary tubes (Q - 1 mm) ; the volume of sample used in each experiment is approximately 30 ~1. The diameter of the tubes and thus the thickness of the sample is determined by the X-ray absorption measured with the tubes filled with water. The diameter is also

checked by direct measurement with a microscope. The X-ray experiments were made under dim red light, at 20°C ; no bleaching occurred during the experiments.

3. Theoretical Treatment of the X-ray Scattering Experiments Our treatment is given within the theoretical framework developed recently for the study of macromolecular systems in solution using solvents of variable density (Luzzati et al., 1976). We shall use the following notation (see also Luzzati, 1960) : s = 2 sin B/h

where 28 is the scattering h = 1.54 A).

angle, h is the wavelength

(in this work

E 01 72 v

Energy of the incident beam, thickness 7 of the sample per cm2), a physical constant v = A2 x 7.9 x 10 - 26.

1, *

Partial specific volume (cm3 g - l) and partial electronic volume (A3 per electron) in water.

c, c,

Concentration, c, in grams of solute per gram of solution, c, in number of electrons of solute per number of electrons of solution.

PW

Distribution AZ).

v, P

Volume of the sample (in Q3) and average of p(r) over ‘Ir.

N

Number of solute particles in the volume I’ of the sample.

(in electrons

of the electron density in the sample (in electrons per

A RHODOPSIN-DETERGENT

COMPLEX

387

m, M

Number of electrons and weight (in daltons) of one particle of solute, unsolvated.

f h% dr)

Electron density distribution of one particle of solute and shape function whose value is 1 inside the particle, 0 outside.

211,Pl

Volume of one particle (wl = J”wl(r) dv,) and average of pi(r) over vl. p1 will also be called buoyant electron density.

PO> 40

Electron density of the solvent and electron density contrast:

Ap,

= PO - A. il(S> PO)

Intensity

corresponding to one particle in a solvent of density po.

Wo)

Radius of gyration of one particle in a solvent of density po.

R,

Radius of gyration of the shape function vl(r).

The whole of the theoretical treatment is based upon two assumptions (see Luzzati et al., 1976). (1) The sample is a perfect solution of identical partioles. (2) The electron density inside the particles-namely over the volume vl(r) impenetrable to the sucrose used to raise the density of the solvent-is independent of the electron density of the solvent. The validity of these assumptions will be discussed throughout this paper and will be shown to be consistent with the whole of the experimental results. The effects of density heterogeneities are discussed in the Appendix. The intensities recorded in the experiments described in this work are rather weak (see Results, section (b)). Indeed, the rhodopsin-detergent complex and the detergent micelles are poor scatterers. Moreover, under our experimental conditions we were unable to raise the concentration beyond 10 mg rhodopsin per ml. Therefore in most experiments only the intensity at very small angles is usable and only two parameters can be extracted from each experimental curve : the value and curvature at s = 0 (see Table 1). Moreover only at p. rather far from p1 could we perform reliable measurements. (a) Zero-angle

intensity

Since the scattered intensity I(s,po) is compared with the energy of the incident beam, and the thickness of the sample is measured, the experimental curves can be normalized and put on an absolute scale (sample scale according to Luzzati et al., 1976; see also Luzzati, 1960). a%Po) = mPo)/?l~~o = &(Qo)l~P.

(1)

It is worth stressing that the first expression of i,(s,po) in equation (1) is purely operational and takes into account the whole of the experimental conditions, whereas the second expression involves only the internal structure of the sample. In the case of a two-component system, which is met here when the solvent does not contain sucrose, i,(O,pHzo) takes the form (Luzzati, 1960): GKbHzO) = mc,(l - P~,~V.

(2)

Thus if the concentration and the partial electronic volume are known in addition

388

C. SARDET,

A. TARDIEU

AND

V. LUZZATI

to i,,(O,p&, equation (2) can be used to determine the number of electrons m, and hence the weight M, of the unsolvated particle. Introducing the conditions : G(O,P,) = 4Pl

- Pd2

c, = mN/Vp

(3) (4)

into equations (1) and (2) leads to the following expression of i,(O,p,) : CG(O~P~W

= Gh

-

p&4-+.

(5)

Equation (5) defines a linear relationship between the (experimental) parameter [i,,(O,p,,/cJ)* and po; its intercept with the p0 axis and its slope deiine the values of p1 and of v,m-3. If m is known (see eqn (2)) the value of v1 can be determined. It is worth noting that if the scattering curves are known from s = 0 to infinity, the value of v1 can be determined independently (Luzzati et al., 1976). In this case the X-ray scattering experiments alone would allow a determination of the value of m, without involving $I. It must be stressed that in equation (5) the parameters p, and v1 refer to the solvated particle. The solvation ratio CC,defined as the number of electrons of water associated with one particle (i.e. contained in the volume vl) to the number of electrons of one unsolvated particle, can also be determined. a = (vh)

- 1,

(6)

(b) Radius of gyration No absolute scale is involved in the determination of the radii of gyration; the analysis requires the knowledge of p1 (see section (a), above and the Appendix). The expression for the radius of gyration as a function of the density of the solvent is (Luzzati et al., 1976) : R2(po) = 3: - alAp

-

V(dpd2,

(7)

where

In equation (8) the origin of r is taken at the centre of gravity of v,(r); equation (9) is independent of the origin of r, The terms a and 6 depend on the internal structure of the sample. a takes into account the relative distribution of the high- and low-density regions inside the particle; for example (see below) its sign indicates whether the high-density moiety is located preferentially in the outer (a > 0) or inner (a < 0) region of the particle. b is a function of the symmetry of the internal structure and more precisely of the distance between the centres of gravity of specific regions of the particle. Indeed if [pl(r) - pl] is decomposed into two parts pa(r) and pb(r), whose centres of gravity are located at ra and rp, b takes the form:

(10) since

.fhW - ,Ud~, = ~I&@)+ pdr)ldv, = 0.

(11)

A RHODOPSIN-DETERGENT

COMPLEX

389

4. Results (a) Biochemical aruEphyaiw-chemical characterization of the complex (i) Chemical composition The procedure described above gives good yields of well-purified rhodopsin. We reproducibly obtain rhodopsin preparations with spectral ratios Azeonm/Asoonm<1*75 and A 400~llllA500~ltl < 0.20. In addition the preparations are virtually free of lipids since we detect less than one phosphorus per rhodopsin. The absorption of rhodopsin on the second hydroxylapatite column permits complete exchange of Ammonyx LO for DDAO and control over the concentration of free detergent in solution (namely detergent not bound to rhodopsin). Rhodopsin is eluted by phosphate as a sharp peak in concentrated form, associated with stoichiometric amounts of detergent above the baseline level of 2 mg DDAO/ml in the eluant, as shown in Figure 1. With this level of free detergent (more than 4 times the critical micellar concentration of DDAO) 1 mg of rhodopsin binds 0*916f0.015 mg of DDAO. This corresponds to a binding of 156 molecules of detergent (N, = 229) per rhodopsin (M, = 39,106). In order to check the effect of sucrose on DDAO binding we carried out one experiment as described above in the presence of 50% sucrose and 2 mg free DDAO/ml. In this case rhodopsin is eluted with 143 molecules of DDAO per rhodopsin molecule. Therefore we concluded that sucrose has a very small influence, if any, on binding.

Pm. 1. Binding of DDAO to rhodopsin. Rhodopsin delipidated and purified is retained on a mirmnum of hydroxylapatite absorbant. The column is eluted with Im buffer containing 2 mg [iW]DDAO/ml until a stable base line of radioactivity is observed. Rhodopsin is then detached with 160 mM-phosphate in the eluant. Fractions of 0.4 ml are collected, rhodopsin and DDAO concentrations are measured from absorbance at 500 nm and radioactivity, respectively. c, concentration; 12,fraction. (0) DDAO; (0) rhodopsin.

(ii) Molecular weight and polydispersity of the rhodopsin-DDAO

complex

When the rhodopsin-DDAO complex is chromatographed on agarose gels in the presence of 2 mg DDAO/ml its elution profile is similar to those of the standard proteins used to calibrate the column (Fig. 2(a)). The proteins used show identical elution positions and profile in the presence and in the absence of detergent in the eluant (except for haemoglobin, which sometimes shows different elution positions). We obtain a Stokes’ radius of 42 L! for the complex, considerably larger than that of the DDAO micelle (23 A) as shown in Figure 2(b). The rhodopsin-DDAO complex sediments as an homogeneous boundary with a sedimentation coefficient (~a~,,,) of I.56 Svedberg units (Fig. 3). We have measured the partial specific volume (e) from the densities of solutions containing rhodopsin

390

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A. TARDIEU

Y (a)

AND

V. LUZZATI

-$ log K,, (b)

FIG. 2. Gel filtration on 10% agctrose. A, cat&se; B, aldolase; C, rhodopsin; D, albumin; E, haemoglobin; F, DDAO mice&s. (a) Rhodopsin or proteins of known Stokes’ radii were deposited on a column containing 10% &g&rose gel beads and eluted with Im buffer with or without 2 mg DDAO/ml. Absorbanoe meesurements of collected fractions indicated the elution position of the various proteins. The elution position of the standard proteins was not perturbed by the presence of DDAO. o, elution volume. (b) Stokes’ radii (R,) of the rhodopsin-DDAO complex and the DDAO micelle. The date of (a) were plotted as described by Andrews (1970) using Stokes’ radii of 52 A for c&&se, 46 A for aldolese, 35 A for albumin and 32 A for haemoglobin (Tanford et al., 1974). R,, is defined as K,, = (V, - V,)/( Vt - V,), V. being the elution volume, V, the exclusion volume (68 ml), and V, the total volume (188.9 ml) of the column.

and dialysates; by the use of [14C]DDA0 we can estimate the binding and therefore the concentration of the complex. Although the experimental data were somewhat scattered, all partial specific volume values were in the range 0.905 to 0.910 cm3/g. An alternative way of estimating the partial specific volume of the complex is to use the additivity rule advocated by Tanford et al. (1974). We measured the DDAO partial specific volume to be 1.122 cm3/g and calculated the partial specific volume of rhodopsin from its amino acid composition (Trayhurn et al., 1974). If one uses Cohn & Edsall’s (1943) values for the partial specific volume of hydrophobic amino acids a value of 0.744 cm3/g is obtained, whereas the value is O-715 cm3/g if one takes the volume occupied by buried hydrophobic amino acids in crystals (Chothia, 1975). Taking these two extreme values, the partial specific volume for the complex is 0.924 cm3/g in one case and O-908 cm3/g in the other.

FIG. 3. Sedimentation of the rhodopsin-DDAO complex. 8 is the sedimentation coefficient (in Svedberg units), c is the rhodopsin concentration (mg/ml). The upper pert of the Figure shows the densitometer tracing of the 600 nm absorbance recorded on the flhn. The position of the moving boundary of the aomplex was recorded at 32min intervals. Underneath is shown the plot of the values of the sediment&ion coeffiient obtained at 2O’C for various protein conoentrations.

A RHODOPSIN-DETERGENT

COMPLEX

391

From Stokes’ radius (R,), sedimentation coefllcient (s~~,~) and partial specific volume (5) the molecular weight (M,) of the complex can be estimated using the equation : M r = Wm,w N &szw,w)(l - %o,w) -l, w in which q20,Wand dao., are the viscosity and density of water at 2O”C, and N is Avogadro’s number. If C = O-905 cm3/g, M, = 76,900, and if v’ = 0.910 cm3/g, M, = 81,100. Therefore, in our experimental conditions (DDAO well above its critical micellar concentration and in its non-ionic form) the data indicate that the complex is a reasonably monodisperse association of one rhodopsin molecule and 156 DDAO molecules. This stoichiometry is barely altered by the presence of sucrose. (b) X-ray scattering experiments We have performed one series of experiments with the detergent micelles and two series with the rhodopsin-detergent complex. The results obtained in the last two series of experiments are very similar; the analysis presented below is based upon the more complete and accurate of the two (see Table 1). In a few cases we tested the hypothesis that the concentration dependence of the scattering curves is negligible within the range of DDAO and complex concentration shown in Table 1. In Figure 4(a) we show an example of the raw data obtained with the complex, and the background scattering due to the micelles of unbound detergent, solvent, capillary tube, etc. In Figure 4(b) we show one family of scattering curves, corrected for background scattering and collimation distortions, obtained with the complex at different sucrose concentrations. The experimental curves were recorded over the range 2*2X 10e3 8-l < s < 4*0X 10m2 A-l, with the exception of the curve in the absence of sucrose which was recorded at 1.75~ low3 A-’ < s < 4.0~ 10-a A-l. The Guinier plots are shown in Figure 5. TABLE

1

Experimental data of the X-ray studyt

DDAO

mice&s

Rhodopsin-DDAO

t See Theoretical 26

complex

Trecttment

A B C D E F G H

0 10.5 19.6 27.9 35.6 43.0 49.9 0 6.0 29.6 33.7 37.8 41.5 45.8 49.5

of the X-ray

0.335, 0.3475 0.357, 0.3692 0.3803 0.3913 0*4027 0.335, 0.3405 0.371 s 0.3777 O-3835 O-3892 0.3961 0.4021 Scattering

20.3, 19.6s 19.08 18.4, 17.96 17.4, 16.g5 15.4s 15.1, 13.3, 13.03 12.7s 12.49 12.1, 11.8,

Experiments.

I.595 4.35.9 7.855 11.41, 16G3g6 18*611 24*248 5.053 3.07, 2~76~ 4*631 8.40s 9.126 11.03, 13.04,

-0 12.6 14.2 14.6 16.0 15.9 15.9 36.4 38.0 18.9 22.3 24.6 25.5 24.4 25.5

392

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s (A-‘) (b) Fm. 4. X-ray scattering curves. (a) An example of raw X-ray scattering experiment, uncorrected for collimation distortions and smoothed. Upper curve: solution of rhodopsin-DDAO complex (experiment H in Table l), exposure time 10 h. Lower curve : the same capillary tube is filled with the solvent containing the same concentration of free DDAO as the solution of oomplex. The two curves are normalized to the same energy of the incident beam; the lower curve thus takes into account the scattering due to solvent, free DDAO micelles, capillary tube, instrument windows and slits, etc. The curve used in subsequent calculations is the difference of the two. n, channel number; N, counts per channel. (b) Intensity curves corrected for background scattering (see above) and collimation distortions, normalized [see eqn (l)), relevant to the rhodopsin-DDAO complex at different sucrose concentrations. The labels A to H refer to the experiments reported in Table 1.

(c) Zero angle intensity

The curves 2/(i,(0,p0)/c,) versus pa (see eqn (5)) are plotted in Figure 6. The experimental points barely depart from straight lines, thus indicating that the particles are homogeneous in density and impenetrable to sucrose (see Appendix). The intercept of the straight lines with the pa axis, which defines the value of pl, is determined quite accurately in the two cases. The accuracy is somewhat higher for the complex since experimental points are available at densities higher and lower than pl. The determination of the particle weights using equation (2) is heavily dependent upon the partial specific volume. Since our measurements (see Results, section (a)) set B for the complex in the range O-905 to 0.910 cm3/g the M, of the complex is between 66,000 and 75,300, which agrees quite well with the chemical determination. In subsequent calculations and in agreement with the binding experiments (see Results, section (a)) we assume that for the complex M, = 74,824, which corresponds to one molecule of rhodopsin and 156 molecules of DDAO ; for this value of M, B = 0.909 cm3/g (see eqn (2)). The partial specific volume of the detergent is known more accurately and equation (2) leads to M, = 16,650 for the micelles; thus each micelle contains 73 DDAO molecules.

A RHODOPSIN-DETERGENT

COMPLEX

I I

I

393

I

I

2

2 ( to-4 a-2 ) Fro.

6. Guinier

plot of the curves of Fig. 4(b).

20-

\

0.

'1

-2o-

\ l

l\

0 \

-4oII

I

I

I I 0.350

PO

PO

(a)

(b)

I

FIG. 6. Plot l/(d,,(O,pO)/c,) z)eww p0 (see eqn (6) and Table 1). The points barely straight lines. The straight lines are determined by linear regression. (a) DDAO micelles (see Table 2). (b) Rhodopsin-DDAO complex (see Table 2).

I

I

I 0.400

depart from

Once r)z is known w1 can be determined from the slope of the straight line (see eqn (5)); when vl, p1 and m are known the hydration ratio u can be calculated using equation (6). The values of these parameters are reported in Table 2. The hydration of the protein in the complex, up, can be estimated on the assumption that the hydration of the polar groups of the detergent is the same in the detergent micelles as in the complex ap = (am - admd)/mp,

(13)

C. SARDET,

394

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TABLE 2

Experimental prameters relevant to the X-ray study Reference

Parameter

(A, per electron) (electrons) DDAO molecules per particle (electrons A-‘) 0% (electrons A - “) (A31

ill,

(A? (electrons

A-“)

69 (electrons

A - 3,

notationt notation eqn (8) notation notation notation eqn (6) eqn (14) ew (16) ew (13) eqn (14) notation w (6)

Detergent micelles

Rhodopsm-detergent complex

3.283 9463 73 6.87 18.4 0*3118 41,170 0.368

(2.746) 41,189 166 8.74 29.6 0.3662 162,900 0.409 74,600 0.4087 0.468 88,300 0.3118 0.368

The molecular weight and number of electrons adopted for rhodopsin = 39,100, m,, = 20,909; and iWp = 229, md = 130. t See Theoretical Treatment of the X-Ray Scattering Experiments.

and for DDAO

are

where ud is the hydration ratio of the detergent micelles (see Table 2), md is the number of electrons of the detergent moiety of one particle of the complex, mP is the number of electrons of one molecule of rhodopsin. If the volume per detergent molecule is assumed to be the same in the micelles and in the complex, the volume v6 of the detergent moiety of the complex can be determined (vd = 41,170 x 156173, see Table 2). Therefore, the volume v, and the average electron density p,, of the protein part of the complex take the forms: VP= VI - Vd

(14)

Pp= m,(l + ~,)/v,.

(15)

(d) Radii of gyration The plot R2(pO) versus (Ap,,)-l is presented in Figure 7 for both the detergent micelles and the complex. The experimental points barely depart from straight lines. This observation is consistent with the hypotheses that the internal structure of the particles is independent of the sucrose concentration and that the particles are homogeneous in density (see Appendix), and with the notion that the position of the centre of gravity is independent of the density of the solvent (see below). The parameters R, (radius of gyration of the shape function) and mze/vl (ratio of the second moment of the density fluctuations and the particle volume) are determined by the slope and intercept of the straight lines fitting the experimental points (see eqns (7), (8)). Since v1 is known (see Results, section (c)) the value of rn,@ can be determined. The values of these parameters are reported in Table 2. The observation that in the two cases m2p is positive indicates that the regions of higher electron density are preferentially located towards the outside of the particles (see eqn (8)).

R2 (p.1 300 -

200 a

100 -

(A p,J-’

20

A3/e (a)

R2 (po)

5OQ-

\ I

I -40

I

0

I

I 40

I

(A pJ

2

a=h (b)

FIQ. 7. Plot R&) versus (dpO)-’ (see eqn (7) and Tables 1 and 2). (a) DDAO mioelles. The term b of eqn (7) is assumed to be 0. The values of R, and map oorresponding to the straight line are reported in Table 2. (b) Rhodopsix-DDAO complex. The term b of eqn (7) is calculated (jpa(r)dv = V& - &), see eqn (10)) and the values of V(dp,) = B2(p0) + b(dp,)- 2 are determined for different distances ra# between the centres of gravity of the protein and of the DDAO regions. A least-squares oalculation of the set V(dp,) uereu-9 (&,,)-I yields the values of Rz and map and the standard error. The straight line corresponds to b = 0 and defines the values of R, and mlp reported in Table 2. The parabolae are the best fit obtained with (rab)a = 26 and 100 Aa, respectively. The statistical - 11, where S.E. is the standard error and the suffix 0 refers to parameter E = [(s,E.)/(s.E.)~ 2 = 0, ia plotted in the insert, aa a function of &: it may be noted that c rises steeply beyond rd r”bs = 60 As.

‘2. SARDET,

392

A. TARDIEU

AND

V. LUZZATI

Equation (10) yields an estimate of the distance between the centres of gravity of the protein and the detergent moieties of the complex. In Figure 7 we show that the best tit of the experimental points with equation (10) corresponds to a distance equal to 0; more careful inspection of the data (see Fig. 7) gives an estimate of the upper limit of the distance at approximately 8 A (see in Appendix the influence of density heterogeneities). Each particle of the complex contains one molecule of rhodopsin, which can be presumed not to contain a large central cavity occupied by the detergent. Therefore, the coincidence of the centres of gravity suggests that the centre of the complex particle is occupied by the rhodopsin molecule and that the detergent molecules, probably held by hydrophobic interactions, cover part of the protein surface. (e) Radiu.s of gyration of the rho&pin

molecules

Taking into account separat,ely the contributions of the protein and the detergent molecules, the expression of the second moment mzp of the complex takes the form :

mzp= .b-“bdr) - G% = Gp - MJ,V~J~ + Jr2[pp(4- &ldv, + (A - ,QG(&)~ + .k2!Ipd(r)- M-k.

(16)

The suffixes p and d refer to protein and detergent, (R,), and (RJa are the radii of gyration of the volumes occupied by the protein and the detergent. We assume here that the centres of gravity of the protein and of the detergent moiety coincide with the centres of gravity of the corresponding volumes and with each other: if this were not the case other terms should be added to equation (16) (we are grateful to Dr P. B. Moore for this remark). Introducing the parameter & (and 4,) (17) and taking into account the equation

~1%= v,(RJ;+ vdRv)i

(18)

and using the numerical values of vl, Rt, mzp, pl, pp and pd (see Table 2) leads to the following expression for (R,): :

NJ; = [vIRkJ[md(v~~~)

-

/jd

+

PI

-

$dl[&

-

pd

+

9%

= 1900(0.0544 - +,)(0.0969 + 4, - $d)-l.

-

$dl-1

(19)

We can now discuss the parameters 4, and $d which allow for the electron density fluctuations inside the protein and the detergent moieties. We assume for the sake of the argument that in each moiety the electron density takes two values; we call Ptwpb? R,, R,, us, vb the electron density levels, radii of gyration and volumes of the low(stix a)- and the high(suffix b)-density regions. Equation (17) takes the form: ‘$d

=

[R:Q(P,

=

(Pb

-

Ijd)(’

Pd) -

+

&dP,

%WuXi).

-

Pdk&

+ %R:)

-’

(20)

In protein molecules the residues tend to be clustered according to the polarity of their side chain (Chothia, 1975). We suppose here that rhodopsin consists of a non-

A RHODOPSIN-DETERGENT

COMPLEX

397

polar region, which contains the residues Val, Ala, De, Leu, Gly, Phe, Pro and a polar region which contains the other residues (and the solvation water). Taking into account the amino acid composition (Trayhurn et al., 1974), the hydrated volume of rhodopsin (see Table 2), and the volumes per residue (Chothia, 1975) we can estimate P,, and pb: pa = 0.3906, p,, = O-4169 electrons Ae3. In rhodopsin the outer part of the molecule is likely to be exposed to water (see below) and therefore the non-polar residues probably are concentrated near the centre of the molecule. In this case R, < R, (see eqn (20)) and the upper and the lower limits of +, can be set at (pb - p,) and 0: 0 < +, < 8.2 x 10e3 electrons A- 3. It may be noted that for myoglobin 4, = 4.5 x 10e3 electrons Am3 (Ibel & Stuhrmann, 1975). The low- and the high-density regions of the detergent moiety can be associated with the hydrocarbon and the polar regions of the DDAO molecules. It is clear that since the distance between the two regions is fixed in each molecule, the ratio RJR” tends to 1 as the size of the detergent moiety increases. We may thus set the lower limit of & at 0 (see eqn (20)). The upper limit of & can be estimated as follows. The rhodopsin molecule is likely to occupy the core of the complex, with part of its surface in contact with the hydrocarbon chains of the detergent (see Results, section (d) and Structure of the Particles, section (b)). Moreover the complex contains a larger number of DDAO molecules than the micelle. Therefore the micelles can be presumed to be more compact than the DDAO moiety of the complex, and the value of 4 observed in the micelles (see Table 2) provides a reasonable estimate of the upper limit of &. In conclusion 0 < & < O-0203 electrons Av3. These values of 4, and & introduced into equations (19) and (18) yield the range of (R,), and (R,Jd : the result is (R,), = 30 (f2.5) d, ( RJd = 29 (h2.5) 8. It may be noted that the values of (R&, and (R& are insensitive to a possible separation of the centres of gravity in the range 0 < rao < 10 A (see Fig. 7). (f) Autowrrelation

functions

The maximum dimension of one particle can be determined by the position of the point where the autocorrelation function-namely the Fourier transform of the intensity-vanishes. We have calculated the autocorrelation functions for the rhodopsindetergent complex in water and in 50% sucrose. The electron density of the latter solvent is very close to the average electron density of the protein, pp, and only the detergent moiety can be expected to be “seen”. The calculation of the autocorrelation function involves the intensity I(s,p,) from s = 0 to inimity; clearly in our experimental conditions the asymptotic trend of I(s,p,,) is difficult to estimate, and the Fourier transforms are likely to be rather inaccurate. Yet it appears (see Fig. 8) that the maximum dimensions are 95 to 115 A for the complex, and 70 to 80 A for the detergent moiety, and thus that the rhodopsin molecules are more elongated than the detergent moiety. Moreover, the autocorrelation function in water, which is the most accurate of the two, displays two interesting features. (It must be noted that in water the electron density contrasts associated with hydrocarbons and protein are of opposite sign.) (a) - P(r) is positive and decreases regularly at r large (region 50 < r < 100 A in Fig. S(a)); this shows that the electron density contrast of the most widely separat*ed regions of the complex is of the same sign, and thus cannot involve protein on one side and detergent on the other. (b) - P(r) has a minimum near 35 4 (see Fig. S(a)), which corresponds to a high concentration of vectors joining

398

C. SARDET,

A. TARDIEU

AND

V. LUZZATI

KM

COO-

500- -

54

:

1

3

0

r(H)

(b)

(a)

FIG. 8. Autocorrelation function P(T). (a) Rhodopsin-DDAO complex in water (experiment A in Table 1). (b) Rhodopsin-DDAO complex in 49.6% sucrose (experiment H in Table 1). The protein moiety is almost matched by the solvent.

hydrocarbon and protein regions. These two features provide strong support for the model discussed in section 5(b).

5. Structure of the Particles (a) The detergent micelles

The analysis of the X-ray scattering experiments leads to five parameters: m, R,, m +, /5,, v1 (see Table 2). We may discuss the structural information which can be obtained from these parameters. The number of electrons, m, defines the number of detergent molecules in the micelle. The sign of mzp indicates that the high density regions-namely the polar groups -are concentrated in the outer part of the micelle. The value of mzp is related to the spatial distribution of the high- and low-density regions. It is possible to draw more precise morphological information by reference to a model. We may suppose that the micelles consist of a hydrocarbon core surrounded by the (solvated) polar groups, that the shape of this core is similar to the external shape of the micelle, and that the electron density distribution is a two-level step-function, one step corresponding to the hydrocarbon, the other to the polar groups. The expression of m,, of this model takes the form:

- P,) m‘h = v,R,2h - PJ - W%h = GC%, - PJ - h - ~aKd~,)~‘~l.

(21)

In equation (21) as well as in the following equations, pa, pbr v,, Q,, n,, nb represent

FIG. 9. Artist’s view of the rhodopsin-lipid interaction in a solution containing rhodopsin and DDAO. Rhodopsin is red: its shape is assumed to be intermediate between a prolate cylinder and a dumb-bell. DDAO molecules are green. The solution contains free DDAO molecules, DDAO micelles and complex particles with one rhodopsin molecule spanning a detergent micelle. The bar in the lower right corner is 50 A long.

A RHODOPSIN-DETERGENT

COMPLEX

399

the electron density level, the volume and the number of electrons of the hydrocarbon (suffix a) and the solvated polar regions (suffix b). We can introduce the following equations : fit% + fbwb = plvl cw %

+

vb

=

(23)

211

pa = n&h

(24)

Y = %I%,

(25)

and a new parameter : Taking into account equations (21) to (25) one obtains the following equation: m,p(v, Rt) - l = (PlY - %bl)(l

- P3)(1

- d-l-

(26)

For a micelle formed by 73 DDAO molecules n, = 7081 electrons. m,,(v,R~) -I is an experimental parameter, whose value is 2.03 x 10e2 (see Table 2). Therefore equation (26) can be solved for y, and the value of v, determined: the result is V~ = 26,473 A”. The volume of the hydrocarbon core can also be estimated from the volumes of the CH, and CR, groups (Reiss-Husson BELuzzati, 1964): the result is 25,623 A3. The excellent agreement of the two figures provides a strong confirmation of the model. The pair of geometrical parameters v1 and R, can provide some information on the shape and size of the micelles. We may assume that the shape is an ellipsoid of revolution ; the volume and radius of gyration allow us to determine the length of the axes (Luzzati et al., 1961). Two ellipsoids are found, an oblate and a prolate: the axes are 258, 55.2, 55.2 A and 34.4, 34.4, 66.4 A, respectively; their surface area corresponds to 88 and 84 A2 per DDAO molecule. With other detergents displaying spherical micelles the radius of the micelles has been found to be close to the extended length of the detergent molecules (Reiss-Husson & Luzzati, 1964). According to this criterion the prolate ellipsoid would be more satisfactory since its short axis is close to twice the extended length of the DDAO molecule. Nevertheless, according to Tanford (1974) most detergent micelles are oblate, not prolate ellipsoids. (b) The rhodopsin-DDAO

complex

Five parameters are determined: m, R,, m2@, pl, ZJ~(see Table 2). The value of m shows that each complex particle contains one molecule of rhodopsin, and yields the number of detergent molecules associated with it. The internal structure of the rhodopsin-DDAO particles is too complex to be discussed in terms of simple models as we did for the DDAO micelles. One hypothesis, which leads to an estimate of the electron density level /r, and of the volume v,, is that the volume and hydration of each DDAO molecule is the same in the micelles and in the complex (see Results, section (c)). of m2eT Ul? Pl$ R,, as well as p,, and v,, were used to estimate the radii of gyration the hydrated protein (R,), and of the volume occupied by the detergent (R,,)* (see Results, section (e)). The coincidence of the centres of gravity of the protein and of the detergent regions (see Results, section (d)) indicates that the two regions are highly symmetrical. Moreover it can be presumed that the rhodopsin molecule occupies the centre of the complex (see Results, section (d) and Fig. 9). The very large value of the ratio (R,)i/ up shows that rhodopsin is highly aniso-

400

C. SARDET,

A. TARDIEU

AND

V. LUZZATI

metric: (R,)& = O-36 (fO.09) for rhodopsin, 0.111 for a sphere. We can envisage a few simple shapes, and use the values of (R,), and v, to determine their size : for example prolate and oblate ellipsoids, prolate and oblate circular cylinders, dumbbell. The lengths of the axes of the ellipsoids would be 33.7, 33.7 (F35), 125 (+25) A and 16.0 (J3), 94.3, 94.3 (f9)A; the diameter and height of the cylinders would be 31.4 (F35), 96.6 (f20) A and 84.2 (-f8), 13.4 (r2.5) A; the maximum length and the diameter of the spheres of the dumb-bell would be 92 (f6), 41.4 A. It is clear that at, least one dimension of the rhodopsin molecule is bound to exceed 80 A; this large dimension agrees with the position of the outer edge of the autocorrelation function (see Fig. 8(a)). We can now look more carefully into the two classes of models, the prolate and the oblate, and try to make a choice. We assume that the DDAO molecules in the complex mimic the lipid environment of rhodopsin in the membrane-more specifically that the hydrophobic interactions are preserved. The possibility of rhodopsin being totally embedded in the lipid with the whole surface covered by the DDAO molecules is easily excluded, since in this case ( RJd would be substantially larger than (R,),. We are thus led to assume that the rhodopsin molecules span a flat detergent’ micelle with one long axis normal, or almost normal to the plane of the micelle, and that the DDAO molecules cover the outer surface of the cross-section of the rhodopsin molecule. Under these conditions if the rhodopsin molecules were oblate in shape the volume occupied by the detergent would extend radially beyond the volume occupied by rhodopsin: the relative values of (RJd and (R,), and the position of the outer edge of the autocorrelation functions (see Results, section (f) and Fig. 8) show that this is not the case. An additional argument against an oblate shape is that the small diameter-16.0 A for an ellipsoid, 13.4 A for a cylinder (see above)-seems too small for a protein. Therefore we conclude that rhodopsin is prolate in shape, with one dimension conspicuously larger than the others. In order to carry out a more precise calculation we may adopt a cylindrical shape of 31.4 A diameter and 96.6 A height (see above), and assume that the shape of the detergent region is an ablate ellipsoid of revolution, with a cylindrical hole in the middle of 31.4 A diameter. Taking into account the volume (wud= 88,300 A3) and the radius of gyration ((R& approx. 29.1 A) of the detergent region it is possible to determine the length of the axes of the ellipsoid : 34 x 80.2 x 80.2 A. The length of the short axis of the ellipsoid is close to twice the extended length of the DDAO molecules, and the area per polar group at the detergent-water interface is 75 A2 ; these two observations agree with the dimensions of the DDAO micelles, and provide support to the model (Fig. 9). Moreover the length of the long axes agrees with the position of the outer edge of the autocorrelation function (see Fig. 8(b)). This model a flat detergent mirelle spanned by an elongated protein molecule, is in excellent agreement with the autocorrelation function (see section 4(f)).

6. Discussion The conclusions of this work are heavily dependent upon the assumptions that the DDAO micelles and the rhodopsin-DDAO particles are monodisperse and that their structure is independent of sucrose concentration. The two assumptions lend themselves to several experimental verifications: (1) the sedimentation and gel filtration behaviour of the rhodopsin-DDAO complex is consistent with the complex being monodisperse (see Results, section (a)) ; (2) the chemical composition of the

A RHODOPSIN-DETERGENT

COMPLEX

401

complex is independent of sucrose (see Results, section (a)); (3) the molecular weight determined by the X-ray and the biochemical studies are so similar that a large polydispersity in weight can be excluded; (4) the linear relationship ~(i,,(s,p,)/c,) versus p,, is consistent with the particles being homogeneous in density and their structure independent of sucrose (see Results, section (c)) ; (5) the linear relationship R2(p0) versus (Ap,,)-l is consistent with the internal structure being independent of sucrose (see Results, section (d)); (6) more generally the internal consistency of the results of the X-ray study and the agreement of the various parameters with the chemical data support the hypotheses made in their derivation. A more detailed analysis of the effects of morphological and density heterogeneities is given in the Appendix. It is worth noting that this type of X-ray study is conditioned by the choice of the detergent. For example Triton Xl90 which we used previously (Osborne et al., 1974) is unsuited to an X-ray scattering study since preliminary experiments showed that the structure of the detergent turns out to be sucrose-dependent; under these circumstances it can be suspected that the rhodopsin-detergent complex is also sensitive to sucrose (one is reminded that the binding of Triton Xl99 by some membranes is known to be lowered by sucrose; Helenius & Simons, 1975; Simons et al., 1973). Most of our analysis is based upon the value and curvature at s = 0 of the X-ray scattering curves measured on an absolute scale. The results of the X-ray study are condensed into the two straight lines ~(in(O,po)/ce) versus p. (Fig. 6) and R2(po) versus (Ap,,)-l (Fig. 7) and therefore lead to the determinetion of four parameters: pl, vllz/m, 4, mph. Moreover, since the partial specific volume is measured, m and v1 are determined. The morphological analysis is based upon these five parameters. Some additional information is provided by the autocorrelation functions (see section 4(f)). The structural analysis of the DDAO micelles is fairly accurate owing to a few simplifying assumptions which allow us to test a specific model. The analysis of the rhodopsin-DDAO complex is more uncertain. An estimate of the electron density fluctuations in the protein volume leads to the determination of the approximate dimensions of the protein and of the detergent regions, and to a model which consists of a highly elongated rhodopsin molecule which spans a flat detergent micelle (see Fig. 9 and section 4 (f)). It must be noted that energy transfer fluoresoent experiments (Wu t Stryer, 1972 ; Renthal et al., 1973) suggest that rhodopsin is at least 75 A long. Taking into account this experiment and current ideas about membrane proteins, Mu-Ming Poo & Cone (1973) proposed a dumb-bell model of rhodopsin which is akin to the model we put forward in this paper. A small-angle neutron scattering study of rhodopsin dispersed in Ammonyx LO has been summarized in a recent report (Yaeger et al., 1976) : the conclusions are that the radius of gymtion of rhodopsin is 23.4hO.3 A and the distance between the centres of gravity of rhodopsin and detergent is 22f5 8. Although X-rays and neutrons do not “see” exactly the same object, these dimensions-especially the distance between centres of gravity-are difficult to reconcile with the results of our work. The discrepancy can perhaps be explained by the procedure used by Yaeger et al. to determine the separation of the centres of gravity (see Moore et al., 1975) which may be inaccurate in this case (Luzzati t Tardieu, unpublished results). Before entering into a discussion of the possible biological implications of our work we wish to make two comments.

402

C. SARDET,

A. TARDIEU

AND

V. LUZZATI

The first is to stress the coarseness of our analysis, which hinders any useful discussion on the precise shape of the protein molecule, its asymmetry, the possible presence of a water channel, and other problems of vital importance for an understanding of the physiological role of rhodopsin. The second is to raise the question of whether rhodopsin preserves its native structure in the DDAO complex. One piece of information is that the spectral properties and transitions of rhodopsin are unaltered in the presence of DDAO (Applebury et al., 1974) ; this observation indicates that at least the local environment of the chromophore is not drastically altered. The kinetics of proton exchange which are sensitive to protein conformational changes are similar whether rhodopsin is part of the rod outer segment membrane or complexed with DDAO (Osborne, unpublished observations). Moreover proteolytic enzymes are known to cleave rhodopsin into identical fragments when acting on the disc membrane and on the rhodopsin-Triton Xl06 complex (Pober & Stryer, 1975; Sardet, unpublished observations). On the other hand DDAO-solubilized rhodopsin once bleached cannot be regenerated by addition of the chromophore (Stubbs et al., 1976). Although this property has often been accepted as a criterion for testing the structure of native rhodopsin, it may rather be dependent on the state of bleached rhodopsin (Osborne et al., 1974, have shown that bleaching may lead to aggregation of rhodopsin). If some denaturation of rhodopsin occurs upon detergent solubilization this must be reversible since Hong $ Hubbell (1973) have shown that rhodopsin purified in alkyl bromides-the most denaturing detergents according to Stubbs et al. (1976)-regains the ability to regenerate upon bleaching when put back into a phospholipid environment. Circular dichroism of detergent-solubilized rhodopsin has also been studied (Waddell et al., 1976; Stubbs et aZ., 1976). Large variations of the circular dichroism spectra in different detergents have been observed and interpreted to indicate that the detergents affect the interaction of the opsin with the chromophore. Moreover the accessibility and local environment of the SH groups of rhodopsin are perturbed by the solubilization process (Pontus t Delmelle, 1975). In conclusion it is difficult in the absence of more sensitive and specific tests, to settle the question of the extent to which the native structure of rhodopsin is preserved in DDAO. It is worth noting in this context that the sensitivity to detergents varies from protein to protein; many membrane proteins are solubilized by non-ionic detergents without loss of activity (Helenius & Simons, 1975; Robinson & Tanford, 1975; Clarke, 1975; Robinson et al., 1974) but total removal of lipids often leads to denaturation (Helenius & Simons, 1975; Walter t Hasselbach, 1973 ; Rubin & Tzagoloff, 1973). It is currently accepted that detergents, upon interacting with membrane proteins, cover the hydrophobic areas which in situ are in contact with the hydrocarbon chains of the lipids (Helenius & Simons, 1975; Robinson & Tanford, 1975). In accordance with these ideas we can assume that the interaction of DDAO with rhodopsin is predominantly hydrophobic. The dimensions of the detergent region of the complex are consistent with the picture of a flat detergent micelle spanned by one rhodopsin molecule (see Fig. 9). The same type of interaction is likely to occur in the membranes, and probably the rhodopsin molecules span the lipid bilayer and penetrate deeply into the intra- and inter-disc space, with a large area exposed to the aqueous environment. This model suggests some speculations on the structure of retinal discs. For the sake of the argument we may adopt a cylindrical shape for the rhodopsin molecule

A RHODOPSIN-DETERGENT

COMPLEX

403

(see above) and suppose that the protein is uniformly hydrated. Moreover we assume that the rhodopsin molecules are oriented at right-angles to the plane of the membrane and that they span the lipid bilayer symmetrically. The average area of membrane available to each molecule of rhodopsin can be estimated from the position of the equatorial band observed in bovine retinal rods (55 8-l; Chabre, 1975), on the assumption of an hexagonal packing: 2 = 2 x (55)2/2/3=3492 AZ. Since the crosssection of a cylinder is 784 A2 the fractional areas in the plane of the lipid bilayer occupied by lipid and hydrated rhodopsin are 0.78 and 0.22, respectively. The separation of the centres of the pair of lipid bilayers is 90 A in rods (Chabre, 1975). Consequently in this model the rhodopsin molecules protrude deeply into the intradisc space and the molecules of the two opposing membranes come close to each other. Moreover the intra-disc space is so crowded with proteins that no point is more than 20 A away from the surface of a protein molecule. In these conditions the intra-disc medium is likely to be highly perturbed by the proteins; it can thus be wondered to what extent it may be available for osmotically free cations.

APPENDIX

Effects of Density Heterogeneities The systems studied in this work are likely to display some degree of heterogeneity. In the micellar solution of DDAO the number of detergent molecules per micelle is not strictly the same for all the micelles (Tanford, 1974), although the density of all the micelles may be expected to be the same. Furthermore, in the complex the number of detergent molecules associated with one molecule of rhodopsin is likely to vary; in this case the density will vary with chemical composition. Although the mathematical treatment given above applies to a solution of identical particles, we have shown (Luzzati et al., 1976) that in the presence of morphological heterogeneities the treatment remains formally correct-some of the parameters being replaced by appropriate average values-provided all the particles have the same density. We wish to analyze here the effects of density heterogeneities. The intensity associated with one particle j in a solvent of density p,, has the expression : il,i(PO+) = G,j (Po - P1.j)” - iw2s2[--bi

- (Po - /%,j)aj

+ (PO- P1.~)2R~,il + . *. . I

(27)

For a solution of N particles i,(p,,,s)/c, takes the form (see eqns (1) to (4)):

1 =,jdl.j(PO,s)/j~l mj.

1 - +wpo) GL(PoP)/Ce = [4L(PoJY/~el [

We introduce the following notation:

+ ...

(28)

Ap, = p. - pc, where pc can be any value

C. SARDET,

404 (see

A. TARDIEU

AND

V.

LUZZATI

below); pl.j = pc + apI.,; X and X are, respectively, the number average and

the vf-weighted

average of X(X = N-l

2 X,; X = 5 vfj Xj/,gl j=l

v&). Equation

5=1

(28) becomes :

~n(PcJwe= 2 [(PO- PC- GlJ2 + 62 P(po) = {[A

+ G

+ (g&]

- 621

+ Apo[-d

(29)

- 26;;;&

+ 6th -1.

+ @Pd2 2WPd2 - 24%~ (30) It is worth noting that equations (29) and (30) are valid without restrictions on the value of pc or the amplitudes of the fluctuations of the various parameters. In what follows we adopt pc = p1 = 0.3562 (see Table 2). We make use of equations (29) and (30) as follows. We transform equation (29) : T(Po)

= ~[~n(Powel

-

6%6$

-

Ghf

= [G(po,O)/% - kl* = &wpo - p1 - $1,. (31) We choose a set of values of the parameter k, and for each value we calculate the term T(po) at each point po. We then treat the set T(p,) versus pO by least squares and we obtain the values of p1 + Spl, of v&ii and of the standard error. The values of the relevant parameters are plotted in Figure Al(a) as a function of a. Similarly we transform equation (30) : VPO)

6h4d21 = A, + (Apt,)-lA, + (AP,)-~& = ~2(poKl

For each value of $$

-

2%1lApo

+

(32)

the treatment of equation (31) (see Fig. Al(a)) provides

the value of &I (it may be noted that Gi is negligibly small) ; we can thus calculate U(Ap,) at each point Ap,. A least-squares treatment of the set U(Ap,) versus (Ape)-l defines the values of A,,, A,, A, and of the standard error. Taking into account the expressions of A,, A, and A, (see eqns (30) and (32)) we introduce the following parameters : R,* = (A,,)+ = (i$ a*=

-A,

-

gl

(33) A, = 6 f Sp,.R,2 - ST,%

A

(341

/----A----

b* = -A, + Splw* + (SP~)~R: A A /--.A = b - Spla + Sp,a * - (SP,)~R:

+

@pA2R:.

(35)

The various parameters are plotted in Figure 10(b) as a function of $. Before discussing the application of these equations to the rhodopsin-DDAO complex we may note that the apparent value of a (a* in eqn (34)) is sensitive to $I

and more seriously that the apparent value of b (b* in eqn (35)) is sensitive to

G1 and 0%

Therefore the determination

of the distance between centres of gravity

I I

I 2K.u’

e/a-= (b)

FIG. Al. Parameters n

obtained

from a least-squares

treatment

function of [(8pl)a]*. (a) T(po) wermL.9po; 808 eqn (31). (b) U(dp,) weraw (dpO)-‘; see eqn (32). Curves (1) and (a), {[s.E./(s.E.)~] - I}, S.E. is the standard

of the experimental

points, as a

n error;

the suffix 0 refers to (3~1)’ =

0. Curve (2),GI ( 10m2 electrons Apa). Curve (3), {[~?/7%(f%/D;)~]t - 1) X 10. Curve (S), r’8, (IO’ Ax2) zz. 1730 b* (see legend of Fig. 7). Curve (6), [n*/(a)0 - 11. Curve (7), {[R:/(R,),] - 1) X 10.

C. SARDET,

406

A. TARDIEU

AND

V. LUZZATI

may well be affected by density heterogeneities. Moreover a statistical analysis of the experimental parameters i&,,O)/ce and B2(p0) should allow us to set a limit to So (see below). The application of the results of the formal analysis to the rhodopsin-DDAO complex leads to the following conclusions. (a) The a dependence of the standard error is less pronounced in Figure Al(a) than in Figure Al(b). This is due to the lack of experimental points in(po,O)/cein the vicinity of p0 = pl, and to the fact that in(po,O)/ce is less accurate than R2(po), since it depends on two additional parameters, concentration and absolute scale. (b) The steep rise of the standp

beyond d(&$

TUN 0.01 (Fig. Al(b)) yields

an estimate of the upper limit of (6~~)~. It may be noted that a variation of p1 in the range 0.3562f0.01 would entail a variation of the number Y of DDAO molecules per rhodopsin molecule from 103 to 239. (c) Within the ranges of c1 and of $$ defined by Figure Al(a) and (b) the parameters a* and b* may be expected not to depart significantly from & and 6 (see eqns (33) to (35)). Moreover within tf‘ (6~~)~< O-012the various parameters of Table 2, calculated with the values of pl, &i?, a* and Rt plotted in Figure Al(a) and (b) turn out to be barely dependent on [ml*. (d) More specifically the separation of the centres of gravity of the protein and the detergent moieties remains very small (rzP < 5 A, see Fig. 7(b)). We thank Drs M. Chabre, A. Helenius, B. Osborne and K. Simons who have discussed this work with us since the beginning, Dr P. Letellier who helped us synthesize DDAO, N. Pasdeloup and M. 0. Moss& for their technical collaboration. One of us (C. S.) was supported during this work by a European Molecular Biology Organization fellowship and more recently by the Commissariat a 1’Energie Atomique. This work was supported in part by a grant of the DBlegation G&&ale a la Recherche Scientifique et Technique. REFERENCES Andrews,

Applebury,

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13, 3448-3458.

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