Detergent micelle structure and micelle-micelle interactions

Size and Shape of Detergent Micelles Determined by Small-Angle X-ray Scattering ... Ben J. Boyd, Calum J. Drummond, Irena Krodkiewska, and Franz Gries...
0 downloads 0 Views 1MB Size
Download PDF
J. Phys. Chem. 1994,98, 10343-10351

10343

Detergent Micelle Structure and Micelle-Micelle Interactions Determined by Small-Angle Neutron Scattering under Solution Conditions Used for Membrane Protein Crystallization P. Thiyagarajan*Jand D. M. Tiede* Intense Pulsed Neutron Source and Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 Received: May 9, 1994; In Final Form: July 25, 1994@

We have characterized micelle structure and intermicelle interaction for the detergents lauryldimethylamine N-oxide, LDAO, and n-octyl-p-D-glucoside, OG, under conditions used for protein crystallization using S A N S . We found that LDAO and OG micelles differ significantly in size, sensitivity to heptanetriol, and nature of intermicelle interactions. Our results suggest that successful crystallization methods can be rationalized in terms of an optimization of micelle size, number density, flexibility of micelle radius of curvature, and suppression of intermicelle interactions. LDAO and OG micelles were found to differ significantly in size and shape. The LDAO micelle was found to be best fit as an ellipsoid with semiaxes of 30.6 and 19.4 A, while the OG micelle was found to be spherical with a radius of 22.9 A. The addition of heptanetriol to pure LDAO resulted in the formation of smaller, spherical, mixed micelles with radii in the range 17-21 A, depending upon conditions. The results suggest that both micelle size and curvature restrictions may contribute to the incompatibility of LDAO for protein crystallization in the absence of additional amphiphiles. The mixed OG-heptanetriol micelle was found to be significantly smaller than that with LDAO, having radii in the range 15-18 A, depending upon conditions, and exhibited a greater number density increase. Evidence was found for interaction between OG and polyethylene glycol, PEG, that prevents micelle aggregation at high ionic strength and likely contributes to the particular success of PEG as a protein precipitant when OG is used as the solubilizing detergent. These measurements suggest that the chemical constituents in membrane protein crystallization can be manipulated to optimize micelle size, number density, and interparticle interactions.

Introduction An understanding of membrane protein crystallization is of central importance to structural biology. Integral membrane proteins require detergent solutions in order to be solubilized in aqueous media. The presence of the detergent greatly complicates the phase map for protein crystallization. The complexity of protein-detergent micelle crystallization arises from the fact that both detergent and protein solubilities are altered by the chemical variables that are used for crystalli~ation.l-~The similarities between procedures used for crystallization of membrane proteins and water-solubleproteins suggest that successful crystallization strategies must find conditions that maximize protein-protein interactions within the crystal while minimizing micelle-micelle interaction^.*-^ For example, success in the use of small amphiphilic molecules in crystallization mixtures has been attributed to the influence that these additives have on micelle size and chemical phase separation t h r e s h o l d ~ . ~ ,However, ~-~ the physical processes underlying crystallization in complex membrane proteindetergent mixtures are not well documented, and recommended procedures for crystallization of membrane proteins still involve a trial-and-error search through a range of variables that include trials using different ionic strengths, precipitants, detergents, and amphiphile~.~-~ Considerable work is needed on the physical mechanisms responsible for membrane protein crystallization in order to establish rational guidelines for crystallization. Bacterial photosynthetic reaction centers provide a useful model for examining mechanisms for membrane protein crystal-

* Address correspondence to this author at: Building 200, Argonne National Laboratory, Argonne, IL 60439. t Intense Pulsed Neutron Source. Chemistry Division. Abstract published in Advance ACS Abstracts, September 1, 1994.

*

@

lization. Reaction centers from two different species, Rhodopseudomonas viridis and Rhodobacter sphaeroides, have been successfully crystallized from detergent mixtures, and their molecular structures have been determined by X-ray7-11 and neutron1*J3diffraction. So far, only two detergents have been found to yield suitable reaction center crystals for high-resolution structural analysis. The structures of these detergents are shown in Figure 1. Lauryldimethylamine N-oxide, LDAO, has been used successfully to produce high-quality crystals of reaction centers, but only in conjunction with the addition of amphiphiles such as heptane-1,2,3-triol or 1,4-dio~ane.'~-l~ Alternatively, n-octylP-D-glucoside, OG, has been used successfully in the absence of additional amphiphiles.17-19 Crystallization in the presence of LDAO was accomplished with a variety of precipitants, including ammonium sulfate,15 potassium ph~sphate,'~ and polyethylene glycol, PEG, sodium chloride mixtures.16,17 The choice of precipitant does not appear to dictate whether crystallization can occur with LDAO as the solubilizing detergent, but the precipitant does appear to alter the unit cell space g r o ~ p . ' ~In, ~contrast, ~ successful crystallization in the presence of OG has only been reported with PEG/sodium chloride mixture~.'~-~O Other membrane proteins have been crystallized in the presence of OG by using salts such as ammonium sulfate as the precipitant,21but these conditions have not yet yielded crystals suitable for X-ray diffraction analysis. These crystallization studies suggest that LDAO, unlike OG, requires the addition of an amphiphile to permit crystallization, while LDAO is less sensitive to the chemical nature of the precipitant than is OG. The unique suitability of PEG/sodium chloride as a precipitant in the presence of OG is also suggested by a comparison of the crystallization of 21 water-soluble proteins in the presence of

0022-365419412098-10343$04.50/0 0 1994 American Chemical Society

10344 J. Phys. Chem., Vol. 98, No. 40, 1994

Figure 1. Chemical structures of the systems considered. The abbreviations are LDAO, lauryldimethylamine N-oxide; OG n-octylB-D-glucoside; PEG, polyethylene glycol; HT, heptane-1,2,3-triol.

OG.22 OG was found to be generally beneficial for crystallization when PEGhodium chloride mixtures were used as the precipitant, but not with ammonium sulfate as a precipitant.22 The cause of the different behavior of LDAO and OG in protein crystallization studies is not known. Dynamic light scattering studies and surface tension measurements have determined how the critical micelle concentration, CMC, cloud point, and micelle size vary for OG as a function of ionic strength and ion type.21s23 However, these studies did not examine the effects of PEG or amphiphiles on these properties. Small-angle neutron scattering, S A N S , has been used to characterize the size and shape of LDAO micelles as a function of heptanetriol con~entration,2~.~~ but the influence of the amphiphile on micelle structure was not examined in the presence of the precipitating agents used in crystallization. We have applied SANS to compare LDAO and OG micelle size and micelle-micelle interactions under the different sets of chemical conditions used for reaction center crystallization. We have examined the effects of sodium chloride, ammonium sulfate, PEG, and heptanetriol additions on LDAO and OG micelle sizes and aggregation states when added alone and in combinations used for reaction center crystallization. These experiments find that LDAO and OG differ significantly in the effect that heptanetriol additions have on micelle size and number density under conditions used for crystallization. These effects are expected to contribute to the different chemical conditions required for reaction center crystallization with these two detergents, and these results suggest ways to optimize these conditions. These studies have also found that the two detergents differ in the nature of the micelle-micelle interaction at low ionic strengths and in the absence of added precipitants. This latter property has implications for protein solvation by these detergents.

Thiyagarajan and Tiede TABLE 1: Relevant Parameters for Systems Considered for SANS scattering chemical density, length density system formula dcm3 x lolo,cm-2 water 'H20 1.o -0.56 heavy water Dz0 1.105 6.358 LDAO CLfi31NO 1.134 -0.221 OG Clfi2806 1.24 0.59 OG (in D20) 1.63 Clfia406 1.24 heptanetriol C7H1603 1.1 0.184 heptanetriol (DzO) C7Hi3D303 1.1 1.54 H(OC2&)wOH 1.02 PEG4000 0.572 10%PEG solution in DzO 1.105 6.11" LDAO + heptanetriol 0.2748b 1.105 mixed micelle From mole fraction. From mole fraction data.25 Barnstead NANOpure purification system before use. All samples were buffered at pH 7 with 10 mh4 potassium phosphate. The samples were prepared fresh and SANS measurements were made within a day. SANS Measurements. The solutions were loaded and sealed in Suprasil cells with a path length of 0.2 cm. S A N S data were measured at 22 "C at the Intense Pulsed Neutron Source of Argonne National Laboratory, using the small-angle diffractometer. This instrument uses pulsed neutrons with wavelengths in the range 0.5- 14 A26and a fixed sample-to-detector distance of 1.54 m. The scattered neutrons are measured by using a 128 x 128 array of position sensitive gas filled 40 x 40 cm2 proportional counter while the wavelengths are measured by time-of-flight by binning the pulse to 67 constant 6th = 0.05 time channels. This instrument thus can provide useful SANS data in the momentum transfer [q = 47c sin(8/1), where 8 is half the scattering angle and 1is the wavelength of the probing neutrons] range 0.007-0.25 A-*. The reduced data for each sample are corrected for the backgrounds from the instrument, Suprasil cell, and the solvent as well as for the detector nonlinearity and were placed on an absolute scale by using the known scattering cross section of a silica gel sample. The absolute cross section for this sample has been measured at D11 and at the SANS instrument at ORNL, which gave almost identical results (R, = 44.7 & 0.2 A, Z(0) = 70 cm-I), and we routinely measure the R, and Z(0) for this sample in the same q region and determine the scale factor for every configuration of the instrument and then apply that scale factor for the other samples. The S A N S data were analyzed by using standard Guinier analysis {ln[Z(q)] vs q2}.27 The slope in the region of qR, 5 1.0 yields the radius of gyration R, of the micelle, and the y-intercept yields Z(O), the scattering intensity at 0" angle. I(0) is proportional to the number density of micelles, Np.

Material and Methods All reagents were purchased from commercial sources and were used without further purification. OG and LDAO were bought from FLUKA, BioChemika grade. PEG 4000, gas chromatography grade, came from Merck (EM Science, NJ). Heptane-1,2,3-triol was obtained from Sigma. The concentrations of these components are described by percentage of the weight of the reagent to the final solution volume (% w/v). Heavy water (99.92% D20) was purchased from Ontario Hydro. The conductivity of this water was less than 0.22 mS/m and total organic content less than 2.3 mg of KMn04 equivalents per liter. The D20 was further processed by passage through a

Here N p and V correspond to the number of particles per unit volume and the volume of the micelles, and emand e, are respectively the scattering length densities of the micelle and the solvent. The values of the constant parameters are given in Table 1. A number of systems included in this study, such as LDAO in DzO and LDAO and OG in PEG solutions, exhibit strong interparticle interactions and hence classical Guinier analysis could not be carried out in the region qR, 5 1.0. Hence nonlinear regression fitting of the scattering profiles was carried out in order to determine both size and shape of the particles formed. The data were fit either with a form factor of a sphere

Detergent Micelle Structure

J. Phys. Chem., Vol. 98, No. 40, 1994 10345

TABLE 2: Size and Number Density of Micelles in 1% LDAO Solutions in DzO from SANS sample apparent R,, A spherical radius, 8, Z(O), cm-I LDAO 18.8 f 0.2 30.6/19.4“ 1.62 f 0.03 LDAO + 0.3M NaCl 18.7 f 0.3 3 1.6/20.0” 1.74 f 0.04 LDAO + 0.1 M NaCl 20.1 f 0.1 35.0119.8“ 1.95 f 0.02 LDAO

+ 1.O M (NI&)zSOd

+

LDAO 5% heptanetriol LDAO 1 M NaCl 5% heptanetriol LDAO 1 M (NI&)zSO4 5% heptanetriol 10% PEG 4000

+ +

LDAO LDAO LDAO LDAO LDAO

+

+

+ 0.3 M NaCl + 1.O M NaCl + 0.3 M NaCl + 5% heptanetriol + 1.0 M NaCl + 5% heptanetriol

25.1 f 0.2 43.0 f 1.0 16.3 f 0.2 16.3 f 0.2 16.3 f 0.2 13.4 f 0.2

21.0 f 0.3 21.0 f 0.3 21.0 f 0.3 17.3 f 0.3

2.63 f 0.2 4.12 f 0.2 1.44 f 0.03 1.47 f 0.03 1.53 f 0.03 0.28 f 0.01

In D20 Solution with 10% PEG 4000 17.9 =k 1.7 30.3/18S0 18.0 f 1.0 29.5/19.0” 18.7 f 1.5 33.0A9.0” 13.3 f 0.2 17.2 f 0.3 13.2 f 0.2 17.0 f 0.3

1.22 f 0.2 1.25 f 0.1 1.55 f 0.2 0.09 f 0.02 1.04 f 0.03

N p x lo”, cm-3 1.42 f 0.01 1.43 f 0.03 1.38 f 0.02 b

b

2.58 f 0.06 2.63 f 0.06 2.75 f 0.06 b

1.61 f 0.26 1.56 i 0.13 ,1.55 f 0.20 5.87 f 0.13 7.08 f 0.21

a In the case of ellipsoidal particles the two semiaxes values are given. Not determined due to either lack of shape information or presence of polydispersity.

(eq 2) or prolate ellipsoid (eq 3), from which Z(0) and the geometrical parameters such as radius (sphere) or semiaxes (ellipsoid) were obtained. In the case of systems whose scattering data permitted Guinier analysis, the values of R, and Z(0) determined were consistent with those from the nonlinear regression analysis fits. Hence we used the fitted geometrical parameters and Z(0) for determining the volume and number density of the particles. The agreement between the parameters derived from Guinier analysis with those determined by the nonlinear regression analysis provides justification for use of this fitting procedure to determine particle volumes in cases of micellar solutions with PEG that could not be analyzed by Guinier analysis due to the presence of strrong interparticle interactions. The functional form used for fitting for a spherical particle was Z(q) = Z(0)[(3 sin qR

+

- qR cos qR)/q3R3)I2 B

f

l i

0

0.5

0.002 0.004 Q.006 s ( A )

0.008

0.01

+

+

(2)

where R and B are the radius of the micelle and the incoherent background. The data which could not be fitted with the spherical form factor were fitted with a form factor corresponding to a prolate ellipsoid and these fitting procedures gave the major and minor axes values and Z(0). The fitted functional form for the form factor for the prolate ellipsoid of revolution averaged for all the orientations in solution was

0

0.002 0.004 $006 9%

0.008

0.01

)

Figure 2. (a, Top) Guinier plots for 1% LDAO (0)and LDAO with 0.3 M NaCl (x) and with 1 M NaCl (A) solutions in DzO. (b, Bottom) Guinier plots for 1% OG (0)and OG with 1 M NaCl (+).

from SANS data collected for LDAO micelles under similar conditions. The discrepancy still remains even after taking into account the fact that our R, value was not determined for infinite contrast. Z(q) = Z(O)Sp”l/J(3 sin X - X cos X)/X3I2 cos ,8d,8 B (3) In an attempt to resolve the differences between these two studies we analyzed the data further as follows. We modeled In eq 3, X = qAs{cos2 ,!? (As/Bs)~sin2 ,!?]1/2 where As and the data in the q region of 0.05-0.2 8,-’ by using the form Bs are the major and minor axes of the prolate ellipsoid and ,!? factors corresponding to spherical (eq 2) and ellipsoidal (eq 3) takes care of orientational averaging. particles. The spherical model fit gave a radius of 24.4 8, and an Z(0) = 1.53 cm-I. The ellipsoidal model gave As = 30.5 f Results 0.5 A, Bs = 19.4 f 0.2 A, and Z(0) = 1.62 cm-’, where As LDAO Solutions. Low Ionic Strength. The results oband Bs are the semiaxes of the ellipsoid. The experimental tained from the above analyses for SANS from LDAO detergent scattering data are plotted in Figure 3 along with the two fits. solutions at various conditions are compiled in Table 2. The The scattering data are fit well by both models. However, the relative sizes of the micelles are characterized by the radius of ellipsoidal model (solid line) appears to fit the data somewhat gyration, R,, obtained from the Guinier plots. The relationship better at high q than does the spherical model (dashed line), between R, and actual molecular dimensions will depend upon even though the experimental uncertainty is relatively high in micellar shape. In order to reduce the effect of the interparticle this region. The slightly better fit of the ellipsoidal shape is interactions on the determination of the apparent R, value for reflected in the residuals for the best fits, which was 1.04 for LDAO solutions, we used data in the q region above 0.05 the ellipsoidal model compared to 1.2 for the spherical form Guinier analysis of the data for 1% LDAO in DzO gave an R, factor. The predicted value of 1.62 cm-’ for Z(0) from the = 18.8 f 0.2 8, and Z(0) = 1.62 cm-’ (Figure 2a). This value ellipsoidal model also more closely matched the experimentally of apparent R, is significantly larger than the value of 16.1 8, determined value of 1.62 cm-’ from Guinier analysis (Figure calculated for infinite contrast by Timmins and c o - w ~ r k e r s ~ ~ . * ~2), than did the value of 1.53 cm-’ predicted from the spherical

+

+

10346 J. Phys. Chem., Vol. 98, No. 40, 1994

Thiyagarajan and Tiede

'

0.01

1.52

u

0.05

0.1

(xi)

0.15

0.2

0

0.002 0.004 J.006 9%

Figure 3. SANS data for the 1% LDAO solution and the fitted data for ellipsoidal (-) and spherical (- - -) particles.

model. Although higher precision measurements are needed in the high-q region in order to definitively characterize the shape of the LDAO micelle, we tentatively conclude that the LDAO micelle is most likely to have an ellipsoidal shape based upon the current findings that the ellipsoidal model is a slightly better fit of both Z(0) and low-q data. This conclusion is supported by the fact that independent,unrestricted fits of scattering data from LDAO micelles in all salt solutions and in the PEG solutions described below consistentlyyield an ellipsoidal shape as the best fit. Also significant is the fact that an anisotropic ellipsoidal shape could not be fit to the LDAO micelles in solutions containing heptanetriol as described later. These finding suggest that even with the relatively low signal-to-noise ratio in the high-q end of the scattering profiles, the data are sufficiently reproducible and the fitting procedures sufficiently sensitive to distinguish between ellipsoidal and spherical shapes. Also the value of 19.4 8, determined for the smaller semiaxis in the ellipsoidal fits agrees well with the 20.3-8, length of the LDAO molecule in its extended conformation. The falloff of ln[Z(q)] for LDAO micelles at low q2 (q2 < 0.005 seen in Guinier plots, Figure 2a, is significant and is characteristic of excluded volume effects arising from interparticle interaction^.^^ This behavior was also previously reported for LDAO micelles under similar low ionic strength

condition^.^^^^^ LDAO Solutions. High Ionic Strength. Increasing the ionic strength of 1% LDAO solutions with NaCl caused marked changes in the SANS profiles. NaCl additions of 0.3 and 1 M caused small but monotonic increases of R, and Z(0) values (see Table 2), and this is due to progressive reduction in the micellemicelle interaction with increasing salt concentration. The nonlinear regression analysis using the ellipsoidal model gave As = 31.6 f 1.2 8, and Bs = 20.0 f 0.5 8, for the LDAO micelle with 0.3 M NaCl and the corresponding values for the 1 M solution were As = 35.0 & 0.4 8, and Bs = 19.8 & 0.1 8,. It is interesting to note that all these samples have almost similar values for the smaller semiaxis, which is very close to the length of the LDAO molecule in its completely stretched conformation. The increase in salt concentration is seen to increase the apparent length of the micelle. The calculated N,, suggests that the number density of micelles is conserved in this salt range. Guinier plots, Figure 2a, show that the increasing salt concentration has a significant influence on the deviation of ln[Z(q)] from a linear dependence on q2 in the low q region. The Guinier plots show that interparticle interactions are essentially removed at 1 M NaC1. This identifies electrostatic repulsion as the cause of the interparticle interaction, which is effectively removed by dielectric screening of the micelle surface charge at high salt concentrations. In contrast to the modest increase in micelle size detected upon addition of 1 M NaC1, the addition of 1 M (NH4)2SO4 was found to cause extensive aggregation of the LDAO micelles. Guinier plots, Figure 4a, show that the aggregated LDAO system

0.008

0.01

)

' e

I

-3

0

0.002 0.004

0.006 0.008

0.01

q2(A'')

Figure 4. (a, Top) Guinier plots for 1% LDAO (0)and LDAO with 1 M (NI-b)2S04 (x) solutions in DzO. (b, Bottom) Guinier plots for 1% OG (0)and OG with 1 M (m)2S04 (A) solutions in D20.

is quite polydisperse, exhibiting at least two linear regions corresponding to R, values of 25.1 f 0.2 8, and 43.0 f 1.0 8,. The shape of the LDAO aggregates could not be determined because of the polydispersity, hence, it was not possible to determine the number of micelle aggregates in this system. However, the important point to note is that these measurements have found that LDAO undergoes extensive aggregation in the presence of 1 M (NH4)2SO4, which is not seen with NaC1. Protein crystallization strategies that use (NH4)2SO4 as a precipitant routinely have (NH4)2SO4 concentrations in the range 1-2 M, and those that use PEG/NaCl mixtures as the precipitant routinely have NaCl concentrations in the range 0.15-0.6 M. Our data show that, in the absence of other chemical additives, these two salts will have different effects on LDAO micelle characteristics which must be taken into account in membrane protein crystallization strategies. LDAO Solutions. With Polyethylene Glycol. Previous S A N S studies have found that scattering can be detected from PEG polymers in aqueous media (Thiyagarajan,P.; Chaiko, D., unpublished). The shape of the scattering profile follows that of a Debye coil due to the polymers themselves and is not due to an aggregation phenomena. PEG4000 shows similar scattering profiles. PEG4000 is typically used as a precipitant in protein crystallization experiments in the concentration range 8%-15% (w/v) together with initial NaCl concentrationsin the range 0.15-0.6 M. Guinier analysis of SANS data for a 10% PEG4000 solution in D20 yields an apparent R, of 13.4 f 0.2 A, Table 2. We point out that under these conditions there exists strong interparticle interactions and thus the R, obtained is smaller than that which can be obtained at lower concentrations of PEG. The scattering data for the mixed system containing the detergent and PEG were analyzed after subtracting the scattering from the pure buffered PEG solution. In the absence of formation of any new particles due to the interaction between the detergent and PEG, the subtracted data should yield results similar to those measured for pure buffered detergent solutions. Figure 5a shows the scattering data measured for the pure buffered PEG solution and the PEG solution containing 1% LDAO along with the subtracted data. Nonlinear regression fitting of the subtracted data in the q region of 0.1-0.2 (Figure 5b) gave semiaxes values of 30.3 and 18.5 8, and an

J. Phys. Chem., Vol. 98, No. 40,1994 10347

Detergent Micelle Structure

0.5 R

0

I

0.002 0.004

0.906 0.008

0.01

qZ(A) -1

0.01

I 0

, 0.05

0.15

X

I

”

-3

0.2

0

0.002 0.004 q‘W’

Figure 5. (a, Top) S A N S data for 10% PEG4000 (x), LDAO and PEG (0)solutions, and the subtracted data (A). (b, Bottom) S A N S data for pure LDAO solution (0)and that in 10% PEG solution ( x ) along with the fits with the ellipsoidal model. Note the decrease in intensity in the low-q region in the case of LDAO in PEG solution, which is due to the increase in interparticle interactions.

Np of 1.61 x IO1’ ~ m - which ~, are similar to those obtained for the pure buffered 1% LDAO solution. The primary difference between the scattering profiles for LDAO micelles in the presence and absence of 10% PEG, shown in Figure 5b, occurs in the low-q region (q < 0.1 A-’), indicating additional excluded volume effects due to the presence of PEG, which is expected to be detected in the SANS experiments. For calculating the number density of the micelles in the PEG solutions we used es = 6.11 x 1Olo cm-2, which has been calculated on the basis of the concentration of PEG and D20 in the solution. The addition of NaCl, up to 1 M, to the LDAOPEG system was found not to appreciably alter the size or number density of the LDAO micelle, Table 2, and they are similar to those noted for pure LDAO solutions. LDAO Solutions. With Heptanetriol. Michel and coworkers have found that additions of the small amphiphile heptane-1,2,3-triol at concentrations of 3-6% (w/v) are critical for crystallizing reaction centers solubilized by LDAO. 14-16 This success suggested the “small amphiphile concept” where the small amphiphiles were proposed to interact with LDAO to form mixed micelles, which are smaller than pure LDAO micelle^.^^^^ This was tested to be true by S A N S studies by Timmins and c o - w ~ r k e r son ~ ~a system of deuterated LDAO and unlabeled heptanetriol. This work determined the molar ratio of LDAO and heptanetriol in mixed micelles. For a 1% LDAO solution with 5% heptanetriol the mole fractions of LDAO and heptanetriol were found to be 0.716 and 0.284, re~pectively.~~ However, in crystallization experiments, heptanetriol is added in combination with protein precipitants. The previous studies did not examine how heptanetriol affects the LDAO micelle under these conditions. These issues are examined below. Figure 6a shows the Guinier plots for 1% LDAO solution in the presence of 5% heptanetriol. The slope of the curve corresponding to LDAO and heptanetriol is smaller than that for LDAO alone, suggesting that the particles are smaller in the presence of heptanetriol. The R, value was determined to be 16.3 f 0.2 8, with an Z(0) of 1.44 cm-’. In contrast to pure buffered 1% LDAO, our modeling with the form factor of a prolate ellipsoid of the SANS data for the mixed LDAOheptanetriol micelles yielded almost similar semiaxes values thus

p.006 0.008

0.01

1

Figure 6. (a, Top) Guinier plots for 1% LDAO (0)and LDAO with 5% heptanetriol (x). (b, Bottom) Guinier plots for the 1% OG (0) and OG with 5% heptanetriol (A).

suggesting a spherical shape. Fitting with a spherical model gave a radius of 21.0 A. This value is very close to that calculated by assuming a spherical model and using the R, determined from the Guinier analysis, as well as to the length of the completely extended LDAO molecule (20.3 A). The changes induced in micelle size and shape upon the addition of heptanetriol to LDAO solutions may indicate a root cause for the requirement of small amphiphile additions for successful crystallization in the presence of LDAO. The droop in the scattering intensity at low q2 shows that the addition of heptanetriol at low ionic strength does not remove the electrostatic, repulsive interparticle interaction. We note that our value for the apparent R, for the mixed micelles in D20 is significantly larger than that reported p r e v i o ~ s l y . ~ ~ Using the previous determination of the mole fraction of LDAO and heptanetriol in the mixed micelle,25we are able to calculate the scattering length density of the mixed micelle needed for the calculation of Np. The calculated volume and the number density of micelles from our S A N S data are 38792 A3 and 2.58 x lo1’ ~ m - respectively. ~, The volume of the mixed micelle is about 75% of that of the micelle in the pure buffered detergent solution, but their number density has increased by about 1.75 from that observed for the pure buffered detergent solutions discussed above. The most remarkable feature of the LDAO system in the presence of heptanetriol is the insensitivity of the mixed micelles to NaCl and (NH4)2SO4 additions. In the presence of heptanetriol, we found that the radius and Np for the mixed micelles are essentially independent of ionic strength and the type of salt used. This was particularly notable for the LDAO micelles following the addition of 1 M (NH4)2SO4. The large aggregates formed in the LDAO solution with (N&)2S04 have broken up into smaller mixed micelles upon adding 5% heptanetriol. This work shows that heptanetriol addition both reduces the size of micelles formed with LDAO and stops the aggregation behavior which would otherwise occur for LDAO micelles in the high ionic strength regimes attained during crystallization. The effect of heptanetriol on LDAO micelle size, shape, and number density is even more prominent in PEG solutions. The spherical mixed micelles of LDAO and heptanetriol were also found to be formed in PEG solutions, but they were appreciably smaller than the mixed micelles formed in the absence of PEG,

Thiyagarajan and Tiede

10348 J. Phys. Chem., Vol. 98, No. 40, 1994 TABLE 3: Size and Number Density of Micelles in 1% OG Solutions of DzO from SANS sample apparent R,, A spherical radius, A I(O), cm-l OG 17.7 f 0.3 22.9 f 0.4 0.237 f 0.005 OG 1 M NaCl 17.1 f 0.3 22.1 f 0.4 0.44 f 0.01 73.0 f 2.0 94.2 f 2.6 2.50 f 0.2 17.2 f 0.3 22.2 f 0.4 0.53 f 0.02 OG 1 M (NH&S04 85.7 f 2.0 110.6 f 2.6 2.65 f 0.2 OG 5% heptanetriol 14.3 f 0.5 18.5 f 0.6 0.24 f 0.05 OG 1 M NaCl 5% heptanetriol 14.2 f 0.4 18.3 f 0.5 0.40 f 0.04 18.2 f 0.5 0.53 f 0.04 OG 1 M (NI-b)2S04 5% heptanetriol 14.1 z!z 0.4 In D20 Solution with 10% PEG 4000 OG 17.0 f 1.5 22.0 f 2.0 0.14 f 0.04 OG 0.3 M NaCl 17.5 f 1.0 22.6 f 1.3 0.20 f 0.01 OG 1.0 M NaCl 18.1 f 0.4 23.4 f 0.5 0.38 f 0.01 OG 0.3 M NaCl 5% heptanetriol 11.2 f 0.6 14.5 f 0.8 0.15 f 0.01 OG 1.O M NaCl 5% heptanetriol 11.6 f 0.3 15.0 f 0.4 0.24 f 0.01

Np x IO”, cm+

+

0.42 f 0.01 0.97 f 0.02

+

1.12 f 0.04

+ + +

1.49 f 0.30 2.58 f 0.26 3.68 f 0.28

+

+

+

+ +

+

+

+

a

a

0.36 f 0.10 0.42 f 0.02 0.66 f 0.02 4.72 f 0.30 6.01 f 0.25

Not determined due to either lack of shape information or the presence of polydispersity.

having a spherical radius of 17.0 f 0.3 A, Table 2. The number density of mixed LDAO-heptanetriol micelles was also found to be higher in the presence of PEG. For example, this can be seen in Table 2 by the 2.7-fold higher mixed micelle concentration in solutions containing 10% PEG and 1 M NaCl compared to the equivalent solution in the absence of PEG. The data in Table 2 show that this enhancement of micelle concentration in PEG-containing solutions was not seen for LDAO micelles in the absence of heptanetriol. OG Solutions. Low Ionic Strength. Thermodynamic properties such as CMC, cloud point, and micelle size were previously determined for OG as a function of its concentration and NaCl by using dynamic light s ~ a t t e r i n g . ~However, ~.~~ effects of heptanetriol, (NH4)2S04, and PEG additions were not included in these studies. This information is necessary for understanding the function of this detergent in membrane protein crystallization. The SANS results for 1% OG solutions in D20 are compiled in Table 3. The Guinier analysis for scattering data for 1% OG in D20 are shown in Figure 2b. This plot yields an R, of 17.7 8, and an I(0) of 0.237 cm-’. The scattering profiles could be fit with a spherical model, having a radius of 22.9 f 0.4 A. This radius is slightly larger than the length of the OG molecule in its extended form. However, our value of micelle radius is consistent with a radius of 23 f 3 8, determined for I % OG at low ionic strength by dynamic light scattering and ultracent r i f u g a t i ~ n . ~The ~ . ~calculation ~ of N p yields a value of 0.42 x 10’’ ~ m - ~The . findings that the OG micelle has a spherical shape while the LDAO micelle has a slightly elongated shape is consistent with observations that elongated shape is often seen for detergents in which the size of the relative head group is relatively small compared to the length of the alkyl tail.30 OG Solutions. High Ionic Strength. In the presence of 1 M NaC1, OG micelles were found to aggregate. A Guinier plot, Figure 2b, shows a linear region with a slope that parallels that for the OG solution in the absence of NaC1. This corresponds to spherical micelle component with a radius of 22.1 0.4 A. ‘Thevertical displacement of the plot of the data for a 1 M NaCl containing sample with respect to the sample without NaCl reflects an increase in the number density of micelles. In the 1 M NaCl sample, Np for the 22 A radius micelle was 0.97 x IOl7 cmT3. In addition, the Guinier plot for the 1 M NaCl sample also suggests a second linear region in the q2range below 0.003, corresponding to an aggregate with an R, of 73 8,. However, the curvature of this plot shows the existence of higher-order aggregates and size polydispersity. Thus NaCl not only reduces the CMC of OG, as described but also induces significant aggregation, although the single micelle is still present.

*

Similarly, the addition of 1 M (NH4)2SO4 instead of NaCl was also found to induce OG micelle aggregation. A Guinier plot of the S A N S data in the presence of (NH&S04, Figure 4b, shows a linear region with a size corresponding to that of a single spherical micelle. In this solution N p is found to be 1.12 x 1017~ m - which ~ , is higher than was found in the case of the OG solution with NaC1, indicating that (NH4)2SO4 is more effective than NaCl in reducing the CMC of OG. The upward curvature of this plot below q2 = 0.003 k2 indicates prominent micelle aggregation and size polydispersity, which is more extensive in.the presence of (NH4)2SO4 than NaCl. It should be noted that this detergent aggregation occurs below the consolution point for each salt, and these detergent solutions were not visibly turbid. OG Solutions with Polyethylene Glycol. In order to examine OG micelle structure in PEG solutions, scattering from the PEG4000 polymer must be subtracted from the detergentcontaining solutions as described above. The subtraction procedure adds uncertainty to the scattering measurement for micelles in PEG solutions compared to pure detergent solutions. In the case of OG micelle, the lower contrast between the micelles and the 10% PEG, D20 solution, Table 1, and the lower micelle number density compared to equivalent LDAO solutions causes the uncertainty to be greater for OG than for LDAO. However, the results given in Table 3 for 1% OG in the absence of heptanetriol show several general features. The most prominent is that the aggregation of OG micelles induced by the addition of 1 M NaCl does not occur in the presence of 10% PEG. Furthermore, the sizes of the OG micelles in PEG solutions remain the same as those seen in the case of pure buffered OG solutions but the number density of the OG micelles has become smaller in the presence of PEG. This could be due to an increase in the CMC by PEG (opposite to the effect of salt) in the case of OG solutions, which is in contrast to that noted for the LDAO solutions. We also observed increases in Np as a function of increasing NaCl concentration even in the case of PEG solutions, but there is no evidence of large aggregates. All these features observed in the case of OG solutions are likely to contribute significantly to the success in using PEG-NaC1 mixtures as precipitants for protein crystallization using OG. We note that comparable measurements cannot be made with 1 M (NH&S04 since this addition causes extensive PEG4000 aggregation and visible turbidity. OG Solutions with Heptanetriol. The small amphiphile, heptanetriol, has dramatic effects on OG solutions. In buffered solutions containing detergent alone and in the presence of NaCl and (NH4)2SO4, the addition of heptanetriol induces changes similar to those seen in LDAO solutions. Heptanetriol was

J. Phys. Chem., Vol. 98, No. 40, I994 10349

Detergent Micelle Structure found to result in the formation of smaller, more numerous mixed micelles than seen in comparable solutions without the heptanetriol. Figure 6b compares Guinier plots for scattering from a 1% OG solution with that measured for a solution containing 1% OG with 5% heptanetriol. The R, values for the OG micelle with heptanetriol is 14.3 k 0.5 A, which is 3.4 8, smaller than for the pure OG micelle, Table 3. The spherical radius and number density of mixed micelles in the solution containing 1% OG and 5% heptanetriol were determined to be 18.5 & 0.6 A and 1.49 x loL7~ m - respectively. ~, From this, the volume of the mixed micelle was found to be about 52% that of pure OG micelles, but N p for the mixed micelle has increased by 3.5-fold. The number density of mixed micelles was obtained by using the scattering length density of OG with all four of its exchangeable protons replaced by deuterium (em = 1.6 x 1O1O cm-2). As a result of the hydrogen exchange in D20, both OG and heptanetriol have similar scattering length densities (see Table 1) and thus the procedure above is justified even though we do not know the molar concentrations of OG and heptanetriol in the mixed micelle. In the presence of either 1 M NaCl or 1 M (NH&S04, the addition of 5% heptanetriol was found to eliminate micelle aggregation and instead formed monodispersed mixed micelles with R, values of 14.2 f 0.4 A, which is equivalent to a spherical radius of 18.3 A. In conjunction with this change in size and uniformity, heptanetriol was also found to increase the number density of mixed micelles to 2.58 x 10" and 3.68 x 10'' cm-3 in presence of 1 M NaCl and 1 M (NH4)2SO4, respectively. Heptanetriol was also found to have a striking effect on OG micelle size in the presence of PEG. OG solutions containing 10% PEG and 5% heptanetriol were found to have very small mixed micelles with a radius of 14.5 A, Table 3. This result is similar to that seen for LDAO, although the radius of the resulting mixed micelle in the case of LDAO is about 2.7 8, larger than that with OG. The number density of mixed OG micelles detected in the presence of PEG was an order of magnitude higher than that seen without it.

Discussion Relevancy to Membrane Protein Crystallization. We have undertaken a characterization of detergent micelle structure and intermicelle interaction under conditions used for protein crystallization using SANS. Currently only the detergents LDAO and OG have been reported to be successful for crystallization of bacterial reaction center proteins for threedimensional structural anal~sis.'~-~O Two characteristic differences are seen in the methods used to crystallize reaction centers using these proteins. First, successful crystallization in the presence of LDAO requires the addition of a small amphiphile like heptane-l,2,3-tri01'~-'~while OG does Second, crystallization in the presence of LDAO can be accomplished with a variety of protein precipitants, including ammonium sulfate and PEG-NaC1 m i x t ~ r e s , ' ~ -while ' ~ high-quality reaction center crystallization with OG has only been reported with PEG-NaC1 mixture^.^^-^^ We have made a comparative study of OG and LDAO micelles under conditions used for reaction center crystallization in order to understand how the crystallization methods modify micelle characteristics to make them compatible with protein crystallization. We have found that LDAO and OG micelles differ significantly in size, sensitivity to heptanetriol, and nature of intermicelle interactions. Our results suggest that successful crystallization methods can be rationalized in terms of an optimization of micelle size, number

L.uryldimetbyl.minbN-oride 19hx32h

Non-Interacting

19hx31A

Elcetrmtatie

21 A Electrostatic

17hor2lh

Non-Interaftinn

I Figure 7. Summary of LDAO micelle structure and intermicelle interaction under solution conditions described in the text. Micelle

size, shape, and number density are represented schematically. For accurate descriptions, see Table 2 and the discussion in the text. density, flexibility of micelle radius of curvature, and suppression of intermicelle interactions, LDAO Micelle Structures. A summary of LDAO micelle structure and intermicelle interactions are shown in Figure 7 for the various solution conditions examined in this paper. LDAO and OG micelles were found to differ significantly in size and shape. The larger LDAO micelle was found to deviate from spherical shape. An ellipsoid with semiaxes of 30.6 and 19.4 8, was fit to the scattering data. We interpret the ellipsoidal shape of the LDAO micelle to reflect restrictions on the radius of curvature for the micelle. Elongated micelle shapes are observed for detergents in which the size of the relative head group is relatively small compared to the length of the alkyl tail.30 In addition, SANS profiles for LDAO showed excluded volume effects, indicative of repulsive, intermicelle interactions. The addition of NaCl to LDAO micelle solutions, in both the presence and absence of PEG, eliminated the repulsive intermicelle interactions, presumably through dielectric screening of electrostatic interactions, but the size and shape of the micelles were unchanged. The fact that crystallization cannot be achieved in LDAO solutions containing PEG and NaCl without the addition of other amphiphiles suggests that the LDAO micelle is incompatible with crystallization under these conditions. The incompatibility could be due to the large size of the micelle or due to the inability of the LDAO micelle to solubilize the reaction center in monodispersed form. The most detailed picture of how detergents solubilize membrane proteins comes from neutron diffraction studies of the detergent phase in reaction center c r y ~ t a l s . ' ~ These J~ studies concluded that the detergent annulus surrounding the reaction center is required to follow a highly variable, locally adaptable radius of curvature due to the convoluted shape of the protein surface.12 The ellipsoidal shape of the LDAO micelle suggests that it has different constraints on micelle curvature compared to OG, which may interfere with proper solvation of the reaction center. SANS studies of deuterated reaction centers in LDAO and OG solutions find that the detergents differ in their ability to support monodispersed reaction center states in the absence of added amphiphiles (Thiyagarajan, P.; Tiede, D. M., unpublished28). This work corroborates the notion that LDAO and OG differ in their solvation of reaction center proteins and will be presented elsewhere.

Thiyagarajan and Tiede

10350 J. Phys. Chem., Vol. 98, No. 40, 1994 n-OCTYGB-D-CLUCOPYRANOSIDE

Non-Interacting

Figure 8. Summary of OG micelle structure and intennicelle interaction under solution conditions described in the text. Micelle size, shape, and number density are represented schematically. For accurate descriptions, see Table 3 and the discussion in the text.

The addition of (NH4)2SO4 to pure LDAO solution caused aggregation of micelles without altering micelle size. Reaction center crystallization is not observed to occur under these conditions. The associative intermicelle interactions operating under these conditions can be expected to interfere with protein crystallization. The addition of heptanetriol was found to result in the formation of spherical, smaller mixed micelles under all conditions. In the absence of other additions, the resulting LDAO-heptanetriol mixed micelle had a radius of 21 A, although repulsive intermicelle interactions were still seen. These intermicelle interactions were removed in mixed micelle solutions at high ionic strength. The radius of the mixed micelle in the presence of PEG and NaCl was 17 A, while a 21 8, radius was seen in the presence of (NH&SO4. These results suggest that the crystallization mixtures that use PEG and NaCl with heptanetriol and the crystallization mixtures that use (NH&S04 with heptanetriol both result in the production of LDAO mixed micelles with similar characteristics that are compatible with crystallization. In each case the resulting mixed micelles are small, spherical, possibly reflecting a flexible radius of curvature, and noninteracting. These features would allow protein-protein contacts to dominate the crystallization process. OG Micelle Structures. The results from SANS studies on OG micelles are summarized in Figure 8. Unlike the LDAO micelle, the OG micelle was found to be spherical, with a radius of 23 A, and exhibited no intermicelle interaction. The addition of NaCl or (NH&S04 caused micelle association and significantly increased the number of micelles. These observations are consistent with previous studies, which showed that thermodynamic properties such as CMC and cloud point of OG solutions are affected by NaCl and (NH&S04 concentrations.21 Surprisingly, the presence of PEG was found to mitigate the effects on NaCl additions on OG micelle properties. While the presence of PEG was found not to alter the size or number density of LDAO micelles, significant changes were seen for OG micelles. The presence of PEG at concentrations used for crystallization was found to eliminate the NaC1-induced aggregation of OG micelles and also diminished the number density of OG micelles. The elimination of OG aggregation suggests that weak interactions may exist between OG and PEG that stabilize the monodispersed micelle. In addition, PEG also appears to enhance the apparent solubility of the OG monomer with respect to the micelle, causing an apparent increase in

CMC. These properties of the OG-PEG interactions are likely to contribute to the unique success of the PEG-NaC1 mixtures as protein precipitants when OG is used as the protein solubilizing detergent. Under these conditions the physicochemical properties of the OG micelle can be seen to be compatible with protein crystallization. The OG micelles have a relatively small size and a flexible radius of curvature as indicated by the spherical micelle shape, and the micelles do not show intermicelle interactions in the presence of PEG. These micelle characteristics are similar to those seen for the mixed LDAO micelles under crystallization conditions discussed above. These studies have also found that the addition of heptanetriol results in the production of smaller, more numerous mixed micelles. The mixed micelles formed between OG and heptanetriol were found to be significantly smaller than the mixed LDAO-heptanetriol micelles formed in comparable solutions. For example, the radius of the spherical OG-heptanetriol mixed micelle was found to be 18.2 and 15 8, in the presence of (NH4)2so4 and PEG-NaC1 mixtures used for crystallization, respectively, compared to the 21 and 17.0 8, radii determined for the LDAO mixed micelles under equivalent conditions. The characteristic differences seen between OG and LDAO mixed micelles formed with heptanetriol are consistent with the properties of other aqueous solutions containing amphiphilic molecules of different solubility, such as lecithin-bile salt31 and phosphatidyl ch~line-anaesthetic~~ solutions. Our finding that OG mixed micelles are smaller than those formed with LDAO can be understood to be due to the smaller solubility difference between OG and heptanetriol than the difference between LDAO and heptanetriol. The ability to produce significantly smaller mixed micelles with OG and heptanetriol compared to LDAO raises the possibility that the smaller OG mixed micelle may be more suitable for crystallization than the LDAO mixed micelle. However, OG and LDAO differ significantly in the extent of increase in the number density of mixed micelles formed in the presence of heptanetriol. Unlike LDAO, the number density of OG mixed micelles was found to increase approximately 10fold compared to that present under equivalent conditions in the absence of heptanetriol. Currently, only one report has described the production of reaction center crystals from OG solutions that contained 1% heptanetriol.20 However, the X-ray diffraction properties of these crystals were no better than those produced without heptanetriol. 17-20 The absence of improvements in reaction center crystallization in the presence of heptanetriol and OG may be a reflection of either the size of the mixed micelle dropping below a lower limit needed for proper solvation of the protein or the interference from the significantly higher number of micelles. Experiments are currently under way to distinguish between these possibilities.

Acknowledgment. This work was supported by NASA Microgravity Biotechnology Program Grant M95 l-ES-3-0042511. This work benefited from the use of the Intense Pulsed Neutron Source, which is funded by the United States Department of Energy, Office of Basic Energy Sciences, under Contract W-31-109-ENG-38 to the University of Chicago. We also acknowledge the technical help provided by D. G. Wozniak at IPNS. References and Notes (1) Zulauf, M. In Crystallization of Membrane Proteins; Michel, H., Ed.;CRC Press: Boca Raton, FL, 1990; p 53. ( 2 ) Garavito, M. R. In Crystallization of Membrane Proteins; Michel, H., Ed.;CRC Ress: Boca Raton, FL,1990; p 89.

Detergent Micelle Structure (3) McPherson, A. In Crystallizafion of Membrane Proteins; Michel, H., Ed.; CRC Press: Boca Raton, FL, 1990; p 1. (4) Michel, H. In Crystallization of Membrane Proteins; Michel, H., Ed.; CRC Press: Boca Raton, FL, 1990 p 73. ( 5 ) Garavito, R. M.; Rosenbusch, J. P. J. Cell Biol. 1980, 86, 327. (6) Michel, H.; Oestorhelt, D. Proc. Natl. Acad. Sci., U S A . 1980, 77, 1280. (7) Allen, J. P.; Feher, G.; Yeates, T. 0.; Komiya, H.; R e s , D. C. Proc. Natl. Acad. Sci. U S A . 1987, 84, 6162. (8) Chang, C.-H.; El-Kabbani, 0.;Tiede, D. M.; Noms, J.; Schiffer, M. Biochemistry 1991, 30, 5352. (9) Deisenhofer, J.; Michel, H. Angew. Chem. Int. Ed. Engl. 1989,28, 829. (10) Miki, K.; Saeda, M.; Masaki, K.; Kasai, N.; Miki, M.; Hayashi, K. J . Mol. Biol. 1986, 191, 579. (11) Yeates, T. 0.; Komiya, H.; Rees, D. C.; Allen, J. P.; Feher, G. Proc. Natl. Acad. Sci. USA. 1987, 84, 6438. (12) Roth, M.; Amoux, B.; Ducruix, A,; Reiss-Husson, F. Biochemistry 1991, 30, 9403. (13) Roth, M.; Lewit-Bentley, A.; Michel, H.; Deisenhofer, J.; Huber, R.; Oesterhelt, D. Nature 1989, 340, 659. (14) Buchanan, S. K.; Fritzsch, G.; Ermler, U.; Michel, H. J . Mol. Biol. 1993, 230, 1311. (15) Michel, H. J . Mol. Biol. 1982, 158, 567. (16) Allen, J. P.; Feher, G. In Crystallization of Membrane Proteins; Michel, H., Ed.; CRC Press: Boca Raton, FL, 1990; p 137. (17) Allen, J. P.; Feher, G. Proc. Natl. Acad. Sci. U S A . 1984,81,4795. (18) Chang, C.-H.; Schiffer, M.; Tiede, D. M.; Smith, U.; Noms, J. R. J . Mol. Biol. 1985, 186, 201.

J. Phys. Chem., Vol. 98, No. 40, 1994 10351 (19) Ducruix, A.; Reiss-Husson, F. J . Mol. Biol. 1987, 193, 419. (20) Franck, H. A.; Taremi, S. S.; Knox, J. R. J. Mol. Biol. 1987, 198, 139. (21) Lorber, B.; DeLucas, L. J.; Bishop, J. B. J . Cryst. Growth 1991, 110, 103. (22) McPherson, A.; Koszelak, S.; Axelrod, H.; Day, J.; Williams, R.; Robinson, L.; McGrath, M.; Cascio, D. J . Biol. Chem. 1986, 261, 1969. (23) Lorber, B.; Bishop, J. B.; DeLucas, L. J. Biochim. Biophys. Acta 1990, 1023, 254. (24) Timmins,P. A.; Leonhard, M.; Weltzien, H. U.; Wacker, T.; Welte, W. FEBS Lett. 1988, 238, 361. (25) Timmins, P. A.; Hauk, J.; Wacker, T.; Welte, W. FEBS Lett. 1991, 280, 115. (26) Thiyagarajan, P.; Epperson, J. E.; Crawford, R. K.; Carpenter, J. M.; Hjelm, R. P. In Proceedings of Intemational Seminar on Structural Investigations on Pulsed Neutron Sources; Dubna, 1993; p 194. (27) Guinier, A.; Fournet, G. Small Angle Scattering; Wiley: New York, 1955. (28) Tiede, D. M.; Thiyagarajan,P.; Noms, J. R. In Surveys of Research in the Chemistry Division; Grazis, B. M., Ed.; Argonne National Laboratov: Argonne, IL, 1993. (29) Michel, H. Trends Biochem. Sci. 1983, 8, 56. (30) Lindman, B.; Wennerstrom, H. Topics Curr. Chem. 1980, 87, 1. (31) Hjelm, R. P. J.; Thiyagarajan, P.; Sivia, D. S.; Lindner, P.; Alkan, H. A.; Schwahn, D. Prog. Colloid Polym. Sci. 1990, 81, 225. (32) Winter, R.; Christman, M.-H.; Bottner, M.; Thiyagarajan, P.; Heenan, R. K. Ber. Bunsenges. Phys. Chem. 1991, 95, 811.