Evidence of Octopolar Symmetry in Bacteriorhodopsin Trimers by

19672

J. Phys. Chem. 1996, 100, 19672-19680

Evidence of Octopolar Symmetry in Bacteriorhodopsin Trimers by Hyper-Rayleigh Scattering from Purple Membrane Suspensions E. Hendrickx, A. Vinckier, K. Clays, and A. Persoons* Center for Research on Molecular Electronics and Photonics, Laboratory of Chemical and Biological Dynamics, UniVersity of LeuVen, Celestijnenlaan 200D, B-3001 HeVerlee (LeuVen), Belgium ReceiVed: May 23, 1996; In Final Form: September 4, 1996X

The hyper-Rayleigh scattering technique has been applied to suspensions of purple membranes, and the size distribution of these membranes, deposited on a mica surface, has been determined by means of atomic force microscopy. A model is developed to express the first hyperpolarizability of a purple membrane fragment in terms of the first hyperpolarizability of the protein bacteriorhodopsin and the angle of the retinal protonated Schiff base with the surface of the membrane. By measuring the depolarization ratio of the scattered secondharmonic light, we deduce a value of (10° ( 1°) for the magnitude of this angle. The arrangement of the proteins in the membrane is found to be predominantly octopolar. Using this angle and the average size of the purple membrane fragments, we find a value of (2000 ( 400) × 10-30 esu for the hyperpolarizability of the protein if we assume that the proteins in a purple membrane patch can be treated as correlated scatterers. Alternatively, using a value of 2100 × 10-30 esu for the hyperpolarizability of the protein, we calculate the average number of proteins in a purple membrane patch (2530). This average is in good agreement with the median (2270) and the average (3470) of the size distribution of the membranes.

I. Introduction Bacteriorhodopsin (bR) is the photosynthetic protein present in the purple membrane of Halobacterium salinarium.1 Upon excitation with visible light, the protein goes through a photocycle during which a proton is pumped from the cytoplasmic side to the extracellular side of the membrane.2 The potential gradient thus established over the purple membrane is used by the bacterium to convert ADP into ATP when the concentration of oxygen is too low to produce ATP by oxidative phosphorylation. The excellent thermal stability of the protein and its unique photochemical properties make bR an excellent candidate for use in optoelectronic devices.3 The structure of the purple membrane and bR has been determined to a resolution of 0.35 nm in the direction parallel to the purple membrane plane by high-resolution electron cryomicroscopy.4 The light-absorbing chromophore present in bR is retinal, which is covalently attached to the protein backbone by means of a protonated Schiff base linkage.5 An experimental study, using the hyper-Rayleigh scattering (HRS) technique, of unbound retinal and several of its derivatives, such as the protonated Schiff base of retinal, has demonstrated that the first hyperpolarizability β of retinal is unusually high and strongly dependent on the solvent of choice.6 Semiempirical calculations, using the intermediate neglect of differential overlap/configuration interaction/sum-over-states (INDO/CI/SOS) method could accurately reproduce the observed tendencies. Since the protonated Schiff base of retinal is present in the bacteriorhodopsin binding pocket, this chromophore is also responsible for the high β of bR. The first hyperpolarizability of bR is an important parameter for the construction of bR-based three-dimensional optical memories.3 Photocontrolled second-harmonic generation by bacteriorhodopsin was reported first by Aktsipetrov et al. in 1987.7 Later, four measurements of the hyperpolarizability of X

Abstract published in AdVance ACS Abstracts, November 15, 1996.

S0022-3654(96)01507-9 CCC: $12.00

bacteriorhodopsin were reported in literature. Second-harmonic generation in poled polymer films gave a value of 2500 × 10-30 esu,8 and a two-photon double-resonance method gave 2250 × 10-30 esu,9 both at a fundamental frequency of 1064 nm. In the second-harmonic generation experiment, a large uncertainty arises from the estimate of the chromophore orientation angle. The two-photon double-resonance method is based on the reduction of a third-order process (two-photon absorption) to a second-order process (second-harmonic generation) under near resonance conditions. Here the derived β value is dependent on the choice of the electronic transition bandwidth. By applying the HRS technique to a completely solubilized sample of purple membranes, we have been able to do a direct measurement of the first hyperpolarizability of the protein.10 The retrieved value of 2100 × 10-30 esu at a fundamental wavelength of 1064 nm is in good agreement with the values measured in the previous two experiments. We also demonstrated the sensitivity of the HRS technique to the state of aggregation of bR, and the decrease in the intensity of the scattered harmonic light by a factor of more than 100 on solubilization was attributed to the annihilation of the orientational correlation between the proteins in the membrane. However, more recent HRS measurements on suspended purple membrane fragments yielded values in the range of 6600-5000 × 10-30 esu.11 This value is based on the assumption that the harmonic fields emitted from bacteriorhodopsin proteins within the same purple membrane fragment are coherent. A vector model is used to relate the hyperpolarizability tensor components of the purple membrane patch to the hyperpolarizability of bacteriorhodopsin, and an estimate is made of the average number of proteins per membrane patch. To investigate this discrepancy, we now focus on the quantitative characterization of the large intensities of frequencydoubled light observed for purple membrane suspensions. Since the structure of the purple membrane has been determined with reasonable accuracy and the theory of correlated scatterers has © 1996 American Chemical Society

Hyper-Rayleigh Scattering Study of bR Trimers been developed for HRS, it should also be possible to determine the first hyperpolarizability of bR by analyzing the HRS signal from a suspension of purple membranes. This analysis can provide new guidelines for the engineering of noncentrosymmetric supramolecular structures with very high optical nonlinearities and can also be used to probe the symmetry and the geometrical arrangement of the chromophores in the membrane. First, we develop a model that allows the expression of the first hyperpolarizability of a typical purple membrane patch in terms of the first hyperpolarizability of monomeric bR and present the theory for the correlated HRS experiment. Atomic force microscopy measurements on purple membrane fragments on a mica surface were performed to determine the average size of a purple membrane patch or the average number of correlated scatterers. The recorded spectral profile of the HRS line clearly shows the absence of multiphoton absorption induced fluorescence. By using the model for the hyperpolarizability of the membranes and measuring the depolarization ratio of the frequency-doubled light, we are able to calculate the angle between the main first-hyperpolarizability tensor component of the protonated Schiff base chromophore and the plane of the membrane. We then deduce a value for the first hyperpolarizability of the protein using the average size of the purple membrane fragments and the angle between the protonated Schiff base chromophore and the plane of the membrane. If we assume that the first hyperpolarizability of the protein is equal to 2100 × 10-30, we can also calculate the average number of proteins per purple membrane fragment. II. Theory (a) First Hyperpolarizability of Purple Membrane Patches. The active nonlinear optical chromophore in the purple membrane patches is the protonated Schiff base of retinal. By measuring the depolarization ratio of the HRS signal of the isolated protonated Schiff base in methanol, we have shown that the first hyperpolarizability tensor of this molecule is dominated by the βzzz component, where z is the direction of the charge-transfer axis.6 Quantumchemical calculations have shown that the charge transfer is directed along the polyene chain for retinal derivatives. Therefore we assume a purely dipolar symmetry for both the protonated Schiff base chromophore and the monomeric protein and model the firsthyperpolarizability tensor of the bacteriorhodopsin protein by a single βzzz tensor component, where z is directed along the polyene chain of the protonated Schiff base of retinal. Measurements using high-electron cryomicroscopy have been used to determine the structure of the purple membrane.4,12 The array of molecules making up these sheets is accurately described as an almost perfect two-dimensional crystal of space group P3 (a ) 6.2 nm) with a dimension of one unit cell only in the direction of the c axis. Three proteins which are in close contact are grouped around the 3-fold axis. The purple membrane can thus be thought of as being composed of trimeric bacteriorhodopsin. As there are three proteins per unit cell, it can easily be calculated that there are nine bR proteins or three bR trimers per 101 nm2 purple membrane. Within a trimer of bR in the purple membrane, the geometry of the retinal protonated Schiff base chromophores is known with less accuracy. The angle between the retinal polyene chain and the plane of the purple membrane has been determined with a variety of techniques. These values are always in the range from 15° to 25°. A value of 20° ( 10° was found with highresolution electron cryomicroscopy on a thin film of purple

J. Phys. Chem., Vol. 100, No. 50, 1996 19673

Figure 1. Top view and side view of the model geometry proposed for the orientation of the three βzzz tensor components of bacteriorhodopsin in the trimer that is the building block of the purple membrane.

membranes.4 Absorption linear dichroism experiments have shown that the angle between the transition moments of the chromophores and the plane of the membrane is 20° for lightadapted bacteriorhodopsin films.13 The geometry we propose for the orientation of the chromophores in the trimer of bR is shown in Figure 1 and is consistent with the structure of the purple membrane deduced by Henderson.4 X, Y, and Z will be used to refer to the reference frame of the trimer, and z is in the direction of the main βzzz tensor component that is parallel to the retinal protonated Schiff base polyene chain. The trimer has C3V symmetry, and the Z axis of the trimer reference frame is chosen parallel to the 3-fold axis. The Y axis of the trimer reference plane is in the mirror plane that bisects the trimer. The only degree of freedom for the chromophores is the angle θ between the βzzz tensor component and the plane of the membrane (0 e θ e π). A similar model was used by Ebrey et al.14 for the analysis of the CD exciton bands of the purple membranes. Group theory and tensor analysis show that the reduction spectrum of the first-hyperpolarizability tensor contains a dipolar and an octopolar term.15,16 Hence molecules for second-order nonlinear optics can be classified as predominantly dipolar or octopolar, depending on the relative importance of the dipolar and octopolar contributions. For purely octopolar molecules, such as these belonging to the D3h point group, all the vectorial properties vanish. Hyper-Rayleigh scattering is the only technique available to determine the first hyperpolarizability of octopolar molecules in solution.27 Because strongly dipolar molecules tend to crystallize in centrosymmetric point groups, the octopolar materials, which do not possess a permanent dipole moment, are excellent candidates for crystallization in noncentrosymmetric point groups. From Figure 1 it is obvious that the situation where θ ) 0 corresponds to a purely octopolar geometry of the chromophores in the membrane (point group D3h) and the situation where θ ) 90° corresponds to a purely

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TABLE 1: Cosine of the Angle between the Main Tensor Component (βzzz) of the Protonated Schiff Bases z1, z2, and z3 and the XYZ Reference Frame of the Trimer z1 z2 z3

X

Y

Z

0 0.866 cos θ -0.866 cos θ

cos θ -0.5 cos θ -0.5 cos θ

sin θ sin θ sin θ

dipolar geometry. In the model proposed by Ebrey et al., the orientation of the chromophores in the trimer is predominantly octopolar. The tensor components of the trimer (T) in the XYZ reference frame can be calculated from this geometry and the βzzz value of the monomeric bR, using

βIJK,T )

∑

[cos(zBI) cos(zBJ) cos(zBK)]βzzz,B

the intensity of the incoherently scattered light at the secondharmonic wavelength that is generated by focusing an intense laser beam in an isotropic solution. A detailed description of the hyper-Rayleigh scattering setup is given in ref 20. On the microscopic scale the intensity of the scattered harmonic light can be connected to the first hyperpolarizability, β. The intensity of the harmonic light scattered by a single, freely rotating molecule (Is) can easily be calculated by applying Hertz’s law and performing an orientational average. If we assume that this molecule has only a single tensor component, βzzz, Is is given by

(1)

B)1,2,3

where zB is in the direction along the main tensor component of the monomer B. The angles between the βzzz tensor components of the monomer and the axis of the trimer reference frame can be determined by simple vector calculus and are given in Table 1. If these are inserted in eq 1, the 11 resulting nonzero tensor components of the trimer are

βXXZ,T ) βXZX,T ) 1.5(cos θ)2(sin θ)βzzz

(2)

βXXY,T ) βXYX,T ) -0.75(cos θ) βzzz 3

βYXX,T ) -0.75(cos θ)3βzzz βYYY,T ) 0.75(cos θ)3βzzz

βZZZ,T ) 3(sin θ)3βzzz Usually, the number of independent components is reduced from 27 to 10 by taking into account intrinsic permutation symmetry (βijk ) βikj) and Kleinman symmetry (βijk ) βkij ) βjki).17 If both conditions apply, the hyperpolarizability tensor is completely symmetrical. Kleinman symmetry is valid only if no absorption occurs and energy is simply exchanged between the fundamental and harmonic field. Even though bacteriorhodopsin is absorbing at the harmonic wavelength (532 nm), the condition βijk ) βkij ) βjki is valid, not due to Kleinman symmetry but to the geometrical arrangement of the chromophores. The hyperpolarizability tensor described by eq 2 is fully symmetrical. As all the trimers have identical orientation in the twodimensional crystal lattice, the tensor components of a purple membrane patch are found by multiplying the tensor components of the trimer by the number of trimers in the purple membrane patch. So far our analysis is similar to that of Schmidt and Rayfield.11 (b) Uncorrelated and Correlated Hyper-Rayleigh Scattering. While first observed in 1965,18 hyper-Rayleigh scattering has emerged as a versatile and convenient method for the determination of the first hyperpolarizabilities of molecules in solution.19 An HRS measurement is performed by measuring

1 2 2 IW Is,U ) B βzzz 35

(4)

B)

32π2

(5)

30cλ4V2

As is the case in linear Rayleigh scattering, the intensity of the scattered harmonic is proportional to the fourth power of the fundamental frequency and inversely proportional to the square of the distance to the scattering molecule (V). If the molecule has a fully symmetrical hyperpolarizability tensor, composed of 10 independent tensor components, the equations for the intensity become

βZXX,T ) 1.5(cos θ)2(sin θ)βzzz βZYY,T ) 1.5(cos θ) (sin θ)βzzz

(3)

where the incident fundamental beam (I) is propagating in the U-direction and is polarized in the W-direction. The frequencydoubled light is observed in the V-direction and polarized in the W-direction and U-direction. The B-coefficient is given by

βYYX,T ) βYXY,T 1.5(cos θ)2(sin θ)βzzz

2

1 2 2 Is,W ) B βzzz IW 7

2 2 〉 IW Is,W ) B〈βWWW

(6)

2 2 〉 IW Is,U ) B〈βUWW

(7)

2 2 〉 and 〈βUWW 〉 are calculated by The expressions for 〈βWWW performing the orientational average over the direction cosines of the transformation from the molecular to the laboratory reference frames.21 For a fully symmetrical hyperpolarizability tensor, these relations are equal to

2 〉) 〈βWWW

1

6

9

2 βiiiβijj + ∑ βiij + ∑ βiii2 + 35 ∑ 7 i 35 i*j i*j

6

12

∑ βiijβjkk + 35βijk2 35 ijk,cycl 2 〉) 〈βUWW

1

2

(8)

11

2 2 βiii βiiiβijj + βiij ∑ ∑ ∑ 35 i 105 i*j 105 i*j

2

8

∑ βiijβjkk + 35βijk2 105 ijk,cycl

(9)

The summations over i * j contain six terms each, and the summation over ijk, cycl contains three terms (βXXYβYZZ, βYYZβZXX, βZZXβXYY), as is also the case with the summation over i. It is clear from this equation that HRS is sensitive to an isotropic average of all the molecular tensor components. Usually, for the determination of the first hyperpolarizability, the sum of the two polarizations is measured. In this case, 2 〉 is defined as 〈βHRS 2 2 2 〉 ) 〈βWWW 〉 + 〈βUWW 〉 〈βHRS

(10)

Hyper-Rayleigh Scattering Study of bR Trimers

J. Phys. Chem., Vol. 100, No. 50, 1996 19675

Figure 2. Vector addition of the scattered harmonic fields. The length of each vector is proportional to the amplitude of the scattered field, and each vector makes an angle δ with the x axis, equal to the phase difference with the harmonic field scattered by a reference molecule. The total scattered intensity is proportional to the square of the magnitude total scattered field Es.

A macroscopic medium will consist of a large number of randomly oriented molecules distributed in space. These molecules will be polarized by the electric field with different phases. The total scattered intensity then is obtained by summing the electric fields scattered by the individual molecules and squaring the result.22 If all the molecules are identical, the fields scattered by the individual molecules will have the same amplitude. This summation can easily be depicted in a phasor diagram (Figure 2). The magnitude of the component of the total scattered field in phase with the field scattered by a reference molecule is

|E Bs0| ) |E Bs,i|∑ cos δi

(11)

i

and the component with a phase angle of 90° is

Bs,i|∑ sin δi |E Bs90| ) |E

(12)

i

The summation is performed over all the molecules in the scattering volume. The total scattered intensity is proportional to the square of the magnitude of the scattered field Es

Bs,1| [(∑ cos δi) + (∑ sin δi) ] Is ) |E 2

2

i

2

(13)

i

with b Es,1 the amplitude of the electric field scattered by a single molecule. By grouping the terms in the summation that can be attributed to a single molecule, we arrive at

Is ∝ Is,1[n + ∑ cos(δi - δj)]

(14)

j*i

with n the number of molecules in the scattering volume and bs,1|2. If the medium is composed of freely rotating Is,1 ) |E molecular scatterers, the value of the second term will fluctuate around the average value of zero. If we neglect this term, the total intensity can be written as the sum of the intensities of the molecular scatterers 2 2 〉f(ω)4 f(2ω)2 IW Is,W ) GN〈βWWW

(15)

2 2 〉f(ω)4 f(2ω)2 IW Is,U ) GN〈βUWW

(16)

G is a constant that groups a number of theoretical and experimental factors. It will be treated as a calibration factor. N is the molecular concentration, and f(ω) and f(2ω) are the local field factors at frequencies ω and 2ω, respectively.

Figure 3. Hyper-Rayleigh scattering depolarization ratio as a function of the angle between the plane of the membrane and the polyene chain of the protonated Schiff base.

If orientational correlations between different molecules exist, the second contribution to the scattered intensity in eq 14 will be different from zero due to the fixed phase relations between the scattered fields. The coherent contribution can be positive as well as negative. This gives rise to a coherent term in the equation for the total intensity 2 2 Is,W ) G[N〈βWWW 〉 + ∑〈βWWW,iβWWW,j〉]f(ω)4 f(2ω)2 IW (17) i*j

2 2 〉 + ∑〈βUWW,iβUWW,j〉]f(ω)4 f(2ω)2 IW (18) Is,U ) G[N〈βUWW i*j

The incoherent part is also given by eqs 8 and 9. In the coherent part an orientational average is made over the correlated scatterers. We have shown that the coherent part can be neglected in solutions of monomeric dipolar chromophores.23 Thus, for a solution composed of noninteracting solvent (S) and solute (s) molecules, the sum of the intensities of U- and W-polarized harmonic fields can be written as 2 2 2 〉S + Ns〈βHRS 〉s)IW Is ) Gf(ω)4 f(2ω)2(NS〈βHRS

(19)

where NS and Ns denote the number densities or the concentrations of the solvent and solute molecules, respectively. However, for a solution of correlated molecules, such as a suspension of purple membranes, the coherent contribution to the harmonic signal has to be taken into account. This can be done by explicitly evaluating the coherent term in eqs 17 and 18, which requires a two-particle correlation function relating the different bacteriorhodopsin proteins.21,24 Ns then is the 2 〉 is a function of concentration of bacteriorhodopsin and 〈βWWW the bacteriorhodopsin tensor component. Another approach would be to consider the harmonic light as generated by a solution of independently moving purple membrane patches. The electric fields scattered by the proteins belonging to the same patch can be added with the same phase. There are no fixed phase relations between the fields emitted by different patches or the proteins belonging to different patches, and thus eq 19 can be written, but with Ns the concentration of purple 2 〉 composed of the tensor compomembrane patches and 〈βHRS nents of a purple membrane patch (eq 2). The concentration of membrane patches can be linked to the number density of bacteriorhodopsin proteins by using the average number of bacteriorhodopsin trimers in a purple membrane patch (ntr)

NPM )

NbR 3ntr

(20)

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Figure 4. Atomic force microscope top view image of purple membranes absorbed on a mica surface.

and eq 19 can be rewritten as

(

2 Is ) Gf(ω)4 f(2ω)2 NS〈βHRS 〉S +

)

NbR 2 〈β 〉 I2 (21) 3ntr HRS PM W

By a similar approach, we were able to analyze the HRS signal from solutions of bis-dipolar 6,6′-disubstituted binaphthol derivatives.25 If the harmonic light is absorbed by the solution, a Lambert-Beer correction term has to be taken into account.26 To avoid this Lambert-Beer correction term, the concentration of bR was kept below 2.0 × 10-6 M. The absorbance of the suspension at 532 nm, for a 1 cm cell, is then smaller than 0.1. (c) Depolarization Ratio of the Scattered Light. To 2 2 2 〉PM, 〈βWWW 〉PM, and 〈βUWW 〉PM, the tensor comdetermine 〈βHRS ponents of eq 2 have to be inserted in eqs 8 and 9. An unknown parameter is the angle between the retinal protonated Schiff base chromophores and the surface of the purple membrane patch (θ). As noted by Schmidt and Rayfield,11 the value for θ can be found by determining the depolarization ratio of the frequency-doubled light scattered by a suspension of purple membranes. This ratio is directly linked to

9 6 54 2 4 54 4 2 y + x y + x y + 0.1286x6 7 35 35 ) (22) 2 9 6 3 〈βUWW〉PM y6 - x2y4 + x4y2 + 0.08571x6 35 35 7

2 〉PM 〈βWWW

with y ) sin θ and x ) cos θ. The product of the calibration constant and the local field factors, the first hyperpolarizability of the bacteriorhodopsin protein, and the average number of trimers per membrane patch cancel. Here we also neglect the second-harmonic signal coming from the solvent, which was measured to be smaller than 1% of the intensity coming from the purple membranes. The graph of the depolarization ratio as a function of θ is given in Figure 3.

If θ ) 0, the three chromophores are lying in the plane of the membrane. This corresponds to a purely octopolar compound, where all the vectorial properties vanish due to the symmetry considerations. For a purely octopolar compound, an HRS depolarization ratio of 1.5 has been reported.27 If θ ) 90°, the three bacteriorhodopsin hyperpolarizability βzzz tensor components are combined in a single βZZZ,T tensor component, corresponding to a purely dipolar compound. For such a compound, as can be seen by taking the ratio of eqs 3 and 4, the HRS depolarization ratio is equal to five. III. Results (a) Atomic Force Microscopy. Atomic force microscopy (AFM)28 is a useful tool for imaging biological samples at high resolution and complements other tools such as NMR and X-ray crystallography. This technique has been applied to study purple membranes, and submolecular details of the individual bacteriorhodopsin proteins have been resolved and interpreted with respect to the atomic model derived from electron microscopy.29 Here we have used atomic force microscopy to determine the average size of the purple membranes. Purple membranes usually appear as patches of about 500 nm diameter and 5 nm thickness. Commercially obtained purple membranes (Sigma/Aldrich) were suspended in water (concentration 1.6 × 10-6 M) and sonicated for 48 h (Branson 2200 sonicator) to reduce the average size of the membranes. A drop of this solution was spread on a freshly cleaved mica surface and allowed to dry in air for 1 h. It had been noticed before that these membranes, suspended in a neutral buffer solution, absorb to freshly cleaved mica. The same solution was then diluted further for the hyperRayleigh scattering experiments. We used a NanoScope III (Digital Instruments) contact mode AFM. The sample was scanned in air, using commercial Si3N4 pyramidal cantilevers with a cone angle of 70° and a spring constant of 0.12 N m-1.

Hyper-Rayleigh Scattering Study of bR Trimers

J. Phys. Chem., Vol. 100, No. 50, 1996 19677

Figure 5. Atomic force microscope section analysis of stacked purple membrane patches. The average height of the observed membranes is 5.5 ( 0.5 nm. The magnitude of the picture corresponds to 1.3 µm × 1.3 µm.

Figure 6. Observed distribution of purple membrane sizes. A total of 178 different membrane patches were measured, and the data was divided over 80 intervals ranging from 0 to 320 000 nm2.

One of the four images used for the determination of the average membrane size is shown in Figure 4. The smallest (a) and the largest dimensions (b) of a total of 178 different patches were measured, and the surface was calculated as (πab)/4. Since the membranes clearly show the tendency to stack on the mica surface, only those membranes that were lying individually on the surface were counted. This stacking is clearly visible in the section analysis shown in Figure 5. The average height of the absorbed membranes is 5.5 ( 0.5 nm. The 178 different sizes were divided into 80 intervals ranging from 0 to 320 000 nm2. This distribution is shown in Figure 6. It can clearly be seen that the largest fraction (74%) of the purple membranes has sizes in the range of 8000-40000 nm2. A small fraction of the membranes (10%), however, has sizes larger than 80 000 nm2. This small fraction makes the distribution asymmetrical and causes the difference between the average particle size (39 000 nm2 or 1150 trimers per membrane) and the median of the distribution (25 500 nm2 or 760 trimers per membrane), since the impact of the small fraction of large membranes is greater on the average than on the median. (b) Hyper-Rayleigh Scattering Measurement. The hyperRayleigh scattering setup, as shown in Figure 7, was used. This setup is sensitive to any light intensity generated by the sample at the harmonic wavelength on a nanosecond time scale. Apart from hyper-Rayleigh scattering, the light intensity at the harmonic wavelength can also be caused by multiphotoninduced fluorescence. It has been shown that two-photon absorption followed by anti-Stokes fluorescence at the secondharmonic wavelength can increase the observed intensity and artificially enhance the calculated value for the first hyper-

Figure 7. Experimental HRS setup: ASL, aspheric lens condenser; B, beam stop; BS, beam sampler; CCM, concave mirror; HW, halfwave plate; INT, 532 nm interference filter; LPF, low-pass filter; M, stepping motor; MI, mirror; ND, neutral density filter; OSC, oscilloscope; PC, personal computer; PCL, plano convex lens; PD, photodiode; PMT, photomultiplier tube; POL, polarizer; RG, high-pass filter; SIG, signal.

polarizability.30 For vitamin A or trans-retinol, a broad emission band, caused by both two- and three-photon absorptions, precluded the observation of the hyper-Rayleigh scattering line.31 Therefore, a verification that the observed intensity indeed is hyper-Rayleigh scattering and not fluorescence is an essential step in the measument procedure. With time-resolved HRS32 or by shifting the fundamental wavelength,33 the hyperpolarizability of fluorescent chromophores can still be determined. To determine the spectral profile of the HRS emission band of the purple membrane suspensions (Figure 8), the interference filter was replaced by a multichannel analyzer. No anti-Stokes fluorescence induced by two-photon absorption or fluorescence induced by three-photon absorption is observed at 532 nm, showing that the observed signal is purely hyper-Rayleigh scattering. The line width is determined by the spectral bandwidth of the multichannel analyzer. To measure the depolarization ratio, the numerical aperture was reduced to approximately 0.1, to avoid signal averaging over directions significantly different from the direction perpendicular to the incident beam.35 An analyzer was placed 2 was directly in front of the photomultiplier, and the ratio Is/IW determined for different angles of the analyzer. The plot of this ratio versus the angle of the analyzer is shown in Figure 9. The depolarization ratio determined from this plot is 1.78 ( 0.08, which corresponds to an angle of 10° ( 1°. Given the number of approximations used, this clearly is a good estimate

19678 J. Phys. Chem., Vol. 100, No. 50, 1996

Hendrickx et al.

Figure 8. Spectral profile of the HRS line obtained by replacing the interference filter by a multichannel analyzer. No fluorescence induced by multiphoton processes can be observed.

Figure 10. Observed linear dependence of the ratio Is/I2W on the concentration of bacteriorhodopsin.

with a known hyperpolarizability, such as p-nitroaniline in methanol (34.5 × 10-30 esu).34 For dipolar molecules, such as p-nitroaniline, it is well-known that βzzz, where z is along the charge-transfer axis, is the most important component of the first-hyperpolarizability tensor.35 In this case the expression for 2 〉PNA reduces to 6/35 (34.5)2. The slope of a similar plot 〈βHRS for a dilution series of p-nitroaniline in methanol was found to be 1290. Note that, at the sensitivity used here, the signal coming from the solvent is not resolved. Using eqs 19 and 24, we can relate the ratio of the slopes to the ratio of the hyperpolarizabilities of p-nitroaniline and bacteriorhodopsin and the average number of trimers per membrane 2 2.004 × 109 0.084ntrβzzz ) 1290 0.171β2

(25)

PNA

Figure 9. Hyper-Rayleigh scattering signal as a function of the analyzer angle. The solid line is a fit to y ) a(cos φ)2 + b. The depolarization ratio then is equal to (a + b)/b. The inset shows a section of Figure 5. A depolarization ratio of 1.78 ( 0.08 leads to an angle between the plane of the membrane and the polyene chain of the protonated Schiff base of 10° ( 1°.

of the angle between the plane of the membrane and the polyene chain. A depolarization ratio of 1.78 clearly indicates that the structure of the nonlinear optical chromophores in the membrane is predominantly octopolar. Next, we insert this value for the angle in the tensor components given in eqs 2, 8, 9, and 10. This gives for 2 〉PM: 〈βHRS 2 2 〈βHRS 〉PM ) 0.252n2trβzzz

(23)

With this relation, eq 21 reduces to

(

2 〉S + Is ) Gf(ω)4 f(2ω)2 NS〈βHRS

)

2 0.252NbRntrβzzz 2 IW 3

(24)

The first term between brackets is dependent on the hyperpolarizability and number density of the solvent molecules. The second term shows that the intensity of the scattered harmonic is proportional to the number density of bacteriorhodopsin and to the number of trimers per purple membrane patch, reflecting the partially correlated nature of the scattered light. 2 versus NbR was determined for a The slope of a plot of Is/IW dilution series of the same suspension of bR in water as used in the AFM measurements and was found to be 2.004 × 109 (Figure 10). The product of the G-factor and the local field factors can be found by measuring this slope for a molecule

where we have assumed that the local field factors for water are identical to those of methanol, which is a good approximation since their indices of refraction are virtually equal (1.329 for methanol and 1.333 for water, both at the sodium D line). If we calculate the hyperpolarizability of the protein, using the average number of trimers per membrane (1150), we arrive at a value of 1800 × 10-30 esu. Alternatively, using the median of the distribution of the number of trimers per membrane (760), we arrive at a value of 2200 × 10-30 esu. If we assume that the largest uncertainty is involved in the estimate of the average number of trimers per membrane, we thus arrive at a value of (2000 ( 400) × 10-30 esu for the hyperpolarizability of bacteriorhodopsin. This is in very good agreement with the previously derived value of 2100 × 10-30 esu for completely solubilized (monomeric) bacteriorhodopsin. If we use the value of 2100 × 10-30 esu for the hyperpolarizability of the protein, we calculate an average number of trimers per membrane of 845, which corresponds to an average membrane surface of 28 400 nm2. IV. Discussion Essential assumptions inherent to the model used are that the purple membranes move independently and that fully constructive interference occurs within a single membrane patch. At a concentration of bR of 10-6 M and for purple membranes composed of 3000 proteins, the average distance between two membranes is about 5 µm. Since this is significantly larger than the average length of the membrane determined by AFM, interaction between the membranes can be neglected. The assumption of emission from a macroscopically isotropic but microscopically anisotropic ordered system is also supported by the work of Andrews and Allcock.36,37 If the interaction between fundamental and harmonic fields extends over distances

Hyper-Rayleigh Scattering Study of bR Trimers larger than the coherence length for frequency doubling, power will oscillate between the fundamental and harmonic fields.17 The average diameter of our purple membrane fragments is 0.2 µm, which is significantly smaller than the estimated value for the coherence length for frequency doubling in the forward direction (25-50 µm).36,37 As an exact value for the first hyperpolarizability of bacteriorhodopsin can be calculated using the proposed model, our results suggest that the dephasing between the fundamental and harmonic fields can be neglected for these small membrane sizes. A similar model for the harmonic light scattered from an aqueous suspension of purple membrane has been reported by Schmidt and Rayfield.11 However, three different values for the angle between the polyene chain and the purple membrane are reported, and the two values reported for the hyperpolarizability of the monomeric protein are not in agreement with the now accepted value of 2100 × 10-30 esu.8-10 We also present more detailed information on the determination of the distribution of the membrane sizes and on the distribution itself, which may account for the discrepancies. Obviously, the calculated value for the hyperpolarizability of bacteriorhodopsin depends on the model geometry and the number of correlated scatterers. The geometry shown in Figure 1 is consistent with earlier structural studies on purple membranes.4 Because accurate values for the first hyperpolarizability of bacteriorhodopsin and for the angle between the membrane plane and the polyene chain can be deduced self-consistently, it is highly likely that the experimental results from hyperRayleigh scattering on purple membrane suspensions can be analyzed using this octopolar model geometry. However, these results do not exclude the unlikely existence of other model geometries or another purple membrane structure that coincidentally would give the same results. Also note that since the equations used here are quadratic, they have both positive and negative solutions. Thus, for the angle between the membrane plane and the polyene chain, -10° is also a correct solution. Similarly, βzzz of the monomeric protein can be -1800 × 10-30 esu. Since both the simple two-state model for β38 and detailed quantumchemical calculations indicate that for dipolar molecules, where the absorption maximum is at higher wavelengths than the wavelength of the frequency-doubled light, β is negative,39 a value of -1800 × 10-30 esu is more likely for the bacteriorhodopsin protein where the absorption maximum is at 568 nm and the wavelength of the frequency-doubled light is at 532 nm. The value determined for the angle between the protonated Schiff base chromophore and the plane of the membrane (10° ( 1°) is in good agreement with other measuments that have yielded values in the range of 20° ( 10°. However, these measurements have been performed on purple membranes lying on various types of solid substrates in different conditions, while the HRS measurement has been performed in solution, at room temperature, and thus is less sensitive to possible conformational changes induced by the substrate or low-temperature conditions. The values determined for the first hyperpolarizability are in excellent agreement with the previously reported value for completely solubilized bacteriorhodopsin (2100 × 10-30 esu), suggesting that the solubilization of the purple membranes by Triton X-100 has only a small effect on the optical properties of the protonated Schiff base. Dencher and Heyn reported that solubilization of purple membrane by Triton X-100 does not lead to a major change in secondary structure.40 These purple membrane patches are an important example of how supramolecular chemistry can be used to enhance the first molecular hyperpolarizability. On the microscopic side it

J. Phys. Chem., Vol. 100, No. 50, 1996 19679 is well-known that the classic donor-acceptor substituted organic conjugated systems41 and the more recently studied octopolar molecules42 have high hyperpolarizabilities. On the macroscopic side, however, the ability to assemble these molecules in noncentrosymmetric phases, such as noncentrosymmetric crystals, poled polymers, or Langmuir-Blodgett films, is, in general, still unsatisfactory. Especially for the octopolar molecules, which do not orient under a static electric field, it is difficult to provide the necessary noncentrosymmetry. If the nonlinear optical chromophores can be incorporated in a supramolecular assembly which results in a thermodynamically stable, noncentrosymmetric structure, this can strongly enhance the second-order nonlinear optical response.43 The purple membranes can be considered as a noncentrosymmetric phase of predominantly octopolar molecules. If we assume that 1150 trimers are incorporated in a membrane and that the hyperpolarizability of a protein is 2100 × 10-30 esu and use a value of 10° for θ, we can calculate a βXXY tensor component of 1.7 × 10-24 esu. The strong enhancement by a factor of 950 is explained by the efficient packing of the proteins in the membrane and not by electronic factors. In conclusion, a model was developed for the geometry of the purple membrane, and the hyper-Rayleigh scattering theory was extended to take into account the correlation between the proteins in the membrane. The model was used to determine a value for the angle between the protonated Schiff base and the plane of the membrane (10°) and to demonstrate the noncentrosymmetric, mainly octopolar, arrangement of the chromophores in the membrane. The average number of proteins per membrane (2530) was determined by atomic force microscopy. Using these data, we determine a β value of 1800 × 10-30 esu for bacteriorhodopsin, in good agreement with the β value of the completely solubilized (monomeric) protein. Acknowledgment. This work is partly supported by the Belgian Prime Minister’s Office of Science Policy “InterUniversity Attraction Pole in Supramolecular Chemistry and Catalysis” (IUAP 16) and the Flemish Government’s GOA 95/ 1. E.H. is indebted to the Research Council of the University of Leuven for a postdoctoral fellowship. K.C. is a senior research associate of the Belgian National Fund for Scientific Research. The research grant for A.V. from “Vlaams Instituut voor de bevordering van het wetenschappelijk-technologisch onderzoek in de industrie (IWT)” is gratefully acknowledged. References and Notes (1) Stoeckenius, W.; Bogomolni, A. Annu. ReV. Biochem. 1982, 52, 587. (2) Mathies, R. A.; Lin, S. W.; Ames, J. B.; Pollard, W. T. Annu. ReV. Biophys. Biophys. Chem. 1991, 20, 491. (3) (a) Oesterhelt, D.; Bra¨uchle, C.; Hampp, N. Q. ReV. Biophys. 1991, 24, 425. (b) Bra¨uchle, C.; Hampp, N.; Oesterhelt, D. Proc. Soc. PhotoOpt. Instrum. Eng. 1993, 1852, 238. (c) Birge, R. R. Am. Sci. 1994, 82, 348. (d) Birge, R. R. Computer 1992, 25, 56. (4) Henderson, R.; Baldwin, J. M.; Ceska, T. A.; Zemlin, F.; Beckman, E.; Douning, K. H. J. Mol. Biol. 1991, 213, 899. (5) Birge, R. R. Annu. ReV. Biophys. Bioeng. 1981, 10, 315. (6) Hendrickx, E.; Clays, K.; Persoons, A.; Dehu, C.; Bre´das, J.-L. J. Am. Chem. Soc. 1995, 117, 3547. (7) Aktsipetrov, O. A.; Akhmediev, N. N.; Vsevolodov, N. N.; Esikov, D. A.; Shutov, D. A. SoV. Phys.-Dokl. (USA) 1987, 32, 219. (8) Huang, J. Y.; Chen, Z.; Lewis, A. J. Phys. Chem. 1989, 93, 3314. (9) Birge, R. R.; Zhang, C. F. J. Chem. Phys. 1990, 92, 7178. (10) Clays, K.; Hendrickx, E.; Triest, M.; Verbiest, T.; Persoons, A.; Dehu, C.; Bre´das, J.-L. Science 1993, 262, 1419. (11) Schmidt, P. K.; Rayfield, G. W. Appl. Opt. 1994, 33, 4286. (12) Henderson, R.; Unwin, P. N. T. Nature 1975, 257, 28. (13) Lin, S. W.; Mathies, R. A. Biophys. J. 1989, 56, 1989. (14) Ebrey, T. G.; Becher, B.; Mao, B.; Kilbride, P.; Honig, B. J. Mol. Biol. 1977, 112, 377 (15) Jerphagon, J. Phys. ReV. B 1970, 2, 1091.

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