refractive index of dark-adapted bacteriorhodopsin and tris(hydroxymethyl)aminomethane buffer...

$: Refractive index of dark-adapted bacteriorhodopsin and tris(hydroxymethyl)aminomethane buffer between 390 and 880 nm$
Refractive index of dark-adapted bacteriorhodopsinand tris(hydroxymethyl)aminomethane buffer

between 390 and 880 nm

Zsuzsanna Heiner1,2 and Károly Osvay1,*1Department of Optics and Quantum Electronics, University of Szeged, P.O. Box 406, Szeged 6701, Hungary

2Institute of Biophysics, Biological Research Center, P.O. Box 521, Szeged 6701, Hungary

*Corresponding author: [email protected]

Received 29 April 2009; revised 10 July 2009; accepted 25 July 2009;posted 27 July 2009 (Doc. ID 110772); published 4 August 2009

The refractivity of wild-type bacteriorhodopsin (bRWT) suspended in tris(hydroxymethyl)aminomethane(TRIS) buffer has been measured in the spectral range of 390–840nm by the method of angle of minimaldeviation with the use of a hollow glass prism. The refractive indices of pure bRWT as well as of TRISbuffer have been determined from the concentration dependent refraction values. Sellmeier-typedispersion equations have been fitted for both the TRIS buffer and pure bRWT. © 2009 Optical Societyof America

OCIS codes: 160.1435, 160.4760.

1. Introduction

In the past 10 years biochemical and biophysicalresearch has aimed at possible applications of bioma-terials. For this purpose the bacterial chromoproteinbacteriorhodopsin (bR) [1] has generated the highestinterest. The light-sensitive chromophore of bR is anall-trans retinal molecule covalently attached to theLysine-216 via a protonated Schiff base. Upon lightabsorption the retinal isomerizes and the proton istranslocated through the membrane via specific ami-no acid groups, while the protein undergoes somespectroscopically separable conformational states(BR, K, L, M, N, O, …). Other absorption maximaand different conformational states (L1 and L2) char-acterize the wild-type bR [2,3], and the macroscopicproperties (for example, refractive index) of wild-typebR show correspondence with bR.The bR and bR-type specimens exhibit very favor-

able linear and nonlinear optical properties such assensitivity to polarization [4,5], considerable changeof refractive index [6,7], high nonlinear optical con-

stants [8,9], naturally occurring photonic crystals[10], and repeatability [11]. Successful experimentshave been carried out to use bR in optical switches,polarization holograms, or second harmonic genera-tion [12–18], in which bR was used in the form of athin film or suspended in some buffer, typically tris(hydroxymethyl)aminomethane (TRIS).

In most of the measurements aiming at the deter-mination of optical properties of bR, the relativechange of refraction index was studied. The absoluterefractive index of dried (or film) bR was determinedat 632nm [12,19] and, in a further experiment, at 11points between 410 and 670 nm [20,21]. Interest-ingly, however, no information is available on thedispersion properties and concentration dependentrefractive index of bR, especially in the near IRrange, where most of the ultrafast lasers operate.

Regarding TRIS, although it is one of the most fre-quently used buffer materials in chemistry, biology,and biophotonics, its dispersion, unlike other sol-vents used in chemistry [22], has not been measuredto our knowledge.

In this paper we report on the measurement ofthe concentration dependent refractive index ofdark-adapted wild-type bR (dissolved in TRIS).

0003-6935/09/234610-06$15.00/0© 2009 Optical Society of America

4610 APPLIED OPTICS / Vol. 48, No. 23 / 10 August 2009

The spectral refractivity of the TRIS buffer is also de-termined, and the refractive index of pure bRWT isthen deducted. To our knowledge, the first Sellme-ier-type dispersion equations are also provided forboth TRIS and pure bRWT for the visible–near infra-red spectral range.

2. Refractive Index of Binary Liquids

In most parts of the spectrum the optical density ofpure bacteriorhodopsin is extremely high, so thedirect measurement of its refractivity is almost im-possible. Our approach was hence to determine therefractive index of bR suspension at different, appro-priately low concentrations, fromwhich the refractiv-ity of pure bR could be obtained.The refractive index of a binary liquid of chemi-

cally nonreactive components can be determinedfrom the refractive index of the constituting compo-nents in several ways. One of the widely used exactforms is the Schwers (or Lattre) form,

nMixðλ;VbRÞ ¼VMix

VbRnbRðλÞ þ

VTRISnTRISðλÞ

; ð1Þ

which is valid for binary liquids without chemical re-action. Here n and V denote the refractive index andthe volume, while the indices Mix, bR, and TRIS re-fer to the bR suspension, the pure bR, and the TRISbuffer, respectively. Hence if one knows the refractiveindex of the solvent, then the refractive index of thesample can be determined from the refractive indexof the suspension.If the sample is highly diluted, then a simpler

method of linear approximation could be used[23,24], where the refractive indices are linearly pro-portional to the percentage of the dissolved samplematerial as

nMixðλ;CbRÞ ¼ αðλÞ · CbR þ nTRISðλÞ; ð2Þwhere the concentration of bR in volume percentageis (CbR), and αðλÞ is a fitting parameter called specificrefractive increment. The refractive index of pure bRis then determined as nbRðλÞ ¼ nMixðλ; 1Þ.

3. Experiment

To determine the refractive indices of the liquid sam-ples, we have chosen a classical yet robust refracto-metry method based on the measurement of theangle of minimal deviation [25]. The sample suspen-sions were filled into a hollow prism, which was theninserted into a goniometer. The eyepiece of the gonio-meter was replaced with a camera sensitive in the

near IR. In order to cover the selected wavelengthrange, two types of light sources have been used(Fig. 1). In the wavelength range of 390–780 nm,the light of a Xe lamp with a power of 1kW was col-limated by achromatic lenses. The required wave-length was selected by an SPM-2 monochromatorhaving a bandwidth of 0:4nm, so that the peak spec-tral power at the sample never excited 60 μW withinthe 390–780nm range. Hence the effect of photo-bleaching [26,27] could be neglected. For the wave-length range of 780–880nm, femtosecond laserpulses from a 70MHz Ti:S laser oscillator were used.A quasi-monochromatic component of the 100nmbandwidth (FWHM) pulses was selected by a JobinYvon H20UV monochromator and then was imagedonto the surface of the hollow prism. The averagepower of the pulse train was around 10 μW at the in-put prism surface, while the peak intensity of a laserpulse was well below 1:183W=cm2. Under such a lowintensity, the multiphoton absorption plays no role;consequently the absorption band remained unaf-fected during the measurement, ensuring that bRstayed in the ground state. All the measurementswere carried out at 22 °C and 42% ambient humidityin total darkness, so the sample was not affected byambient light either.

The purple membranes were centrifuged fromHalobacterium salinarium with the standard proce-dure and put in a deep freezer until use. This concen-trated solution of bR sample still contains very littleintercellular distilled water, while the water contentof the cells is assumed normal. Before our measure-ments the necessary amount of bR samples (concen-trated solution) was melted and kept in ambienttemperature for 3–4 h. In order to obtain close to uni-form trimers, the suspension was dipped into an ul-trasound bath and then diluted to the requiredconcentration in TRIS (10mM, pH 7.0) buffer. At thesuspension concentrations we used, the tiny amountof distilled water originating from the concentratedbR was negligible. The prepared suspension readyFig. 1. (Color online) Complete experimental setup.

Fig. 2. (Color online) Measured refractive index of TRIS with(solid) and without (dashed line) correction for air.

10 August 2009 / Vol. 48, No. 23 / APPLIED OPTICS 4611

for use was kept at room temperature for 6–8 h priorto the measurement. In order to determine the abso-lute concentration of the suspended bR [28], the ab-sorption spectra were recorded.Regarding the measurement procedure, the in-

coming quasi-monochromatic light from either ofthe sources passes through the input slit and the col-limator lens of the goniometer, so that a collimatedbeam propagates through the empty prism. The in-put slit is projected into the plane of the camera by atelescope, and the scale of the goniometer is set tozero. The prism is then filled with the sample liquidand aligned to minimum deviation, while the cameraand telescope assembly is rotated to keep the imageof the slit at the same position on the camera. Theangular position of the assembly is then measuredon the vernier for each spectral line. The minimumdeviation, δ, in a prism occurs when the entering an-gle and the exiting angle are the same, a particularlysymmetrical configuration. Applying Snell's law atthe interfaces, the following relationship can bedefined:

nliq ¼ nair ·sin

�δþφ2

�

sin�φ2

� ; ð3Þ

where nliq is the refractive index of the liquid in thehollow prism, nair is the refractive index of the air,and φ is the angle between the two relevant prismfaces; this angle was measured with the use of aHe–Ne laser, and it was found to be 59:8� 0:0017°.

The error of the measurement is eventually deter-mined by the accuracy of the angle measurement andthe value of the refractive index itself [25]. The errorof the angle measurement is established by the man-ufacturing tolerance of the hollow prism, and theaccuracy of the goniometer in our case resultedin 0:09 arcmin.

The error propagation upon determination of therefractive indices depends on the measured angleof minimum deviation angle and the angle of thehollow prism, as

dn ¼��∂nðδ;ϕÞ

∂δ

��dδþ��∂nðδ;ϕÞ

∂ϕ

��dϕ: ð4Þ

Hence in our case the total error of the refractiveindex measurement varied from 0.0004 (near infra-red) to 0.0003 (near UV).

4. Results

In the experiment we first determined the refractiveindex of the buffer TRIS and then the refractive in-dex of the bR solution. In order to make the measure-ment as precise as possible, the refractive index ofthe solution was measured at different concentra-tions between 0 and 76 μm. The angle of minimal de-viation was usually measured in steps of 10nm. Inthe case of bR samples, in their anomalous dispersionrange of 500–600nm, the step size was refined to5nm. At each wavelength a set of three independentalignment and reading processes was accomplished,resulting in a summarized standard deviation assmall as 0:0017°, in agreement with Ref. [25]. Therefractive index was then determined from Eq. (3),where the dispersion of air under our actual labora-tory environment was computed from a temperatureand pressure dependent Sellmeier equation [29].

A. Refractive Index of TRIS

Figure 2 shows the refractive indices of TRIS deter-mined from the measured angle of the minimum de-viation and refractive index of air. To demonstratethat the presence of ambient air cannot be neglected,the index values obtained by assuming nair ¼ 1 inEq. (3) are also displayed.

For easy handling of the refraction of a sample, it iscustomary to fit dispersion equations to the mea-sured data. Among many refractivity formulas avail-able, we chose the Sellmeier-type equation for tworeasons. First, it is the only semi-empirical disper-sion equation; that is, its basic form can be deductedfrom the Lorentz theory of absorption and disper-sion. Second, both the TRIS buffer and the bR sample

Table 1. Coefficients of Sellmeier Equations of TRIS at the Ambient Pressure and T ¼ 22 °C for Two and Four Parameter Fitting

TRIS (10mM, pH 7.0) A1ð105Þ A2ð109Þ λ1 ½nm� λ2 ½nm�One-term Sellmeier 7.363698414 – 101.0293566 –

Two-term Sellmeier 7.757363056 1.17425171286 98.6571625 1040.2402896

Fig. 3. (Color online) Difference between the measured and fittedrefractive index values of TRIS.


contain relatively large amounts of distilled water.Because of this, the refractive indices are expectedto be relatively close to that of distilled water. Therefractive index of distilled water was very preciselyfitted from UV to NIR by the use of the Sellmeier-type dispersion equation.For TRIS buffer we write the Sellmeier equation in

the form of

n2 − 1 ¼Xk

i¼1

Ai

λ−2 − λ−2i; ð5Þ

where λ is the wavelength measured in nanometers,and Ai and λi are the fitting parameters. To keep theequation as simple as possible, first a one-term equa-tion (k ¼ 1) was fitted with coefficients listed inTable 1. Its deviation from themeasured value (Fig. 3)is unsatisfactorily high. However, a two-term (k ¼ 2),hence four-parameter, Sellmeier form already

matches verywell, providing a standard deviation be-tween themeasured and fitted refractive indexvaluesof less than 1 · 10−4 (Fig. 3). This lies well below theinherent measurement error of 4 · 10−4.

B. Concentration Dependent Refractive Index of bR

As a second step toward determination of the refrac-tive index of pure bR, refractivity of suspensions atten different bR concentrations has been measured.For the sake of clarity, the measured values are dis-played in Fig. 4 for only four concentrations between390nm and 880nm. As one can see, the suspensionsat such a low bR concentration clearly exhibit normaldispersion in the entire wavelength range; that is,the anomalous dispersion of bR around 560nm is ap-parently suppressed. As we see in the next subsec-tion, however, the anomalous dispersion of pure bRcan be deducted from the measurements.

The refractive indices at two wavelengths areshown for all concentrations in Fig. 5. Although

Fig. 4. (Color online) Measured refractive indices of bR suspension at concentrations of 20, 39, 58, and 76 μm. The wavelength range hasbeen split into three parts so that the values due to the different concentrations can be distinguished more easily.

Fig. 5. (Color online) Measured refractive indices of bR as a func-tion of concentration at two different wavelengths: 562nm, aroundthe main absorption line of dark bR; 800nm, with no apparentabsorption.

Fig. 6. (Color online) Refractive index of pure bR obtained fromthe Schwers form (symbols) and the corresponding semi-empiricalSellmeier fit (solid line).


the behavior of the concentration dependence is ba-sically similar for the entire wavelength range, thesetwo wavelengths have been chosen: one lies at thepeak absorption line of dark bR (562nm), and theother one (800nm) is where no absorption can be ex-pected at all. In both cases, similar to all the otherwavelengths, the measured refractive index valuesshow a clear linear dependence on the thickeningof the bR suspension.The full set of measurements was repeated one

week later, starting from the melting and dilutingprocess of a fresh frozen bR sample, described inSection 3. As one may expect, the obtained refractiveindex values have been in excellent agreement withthe previous set of measurements. Hence the refrac-tive index of bR is independent of the production dateof the base sample.The effect of polarization was also checked by ro-

tating the polarization of the laser beam by a half-wave plate. At lower concentrations, no differencewas experienced between the refractive indices mea-sured at the two orthogonal polarizations. Only atthe highest concentration that we used, that is, at76 μM, were the values for the s-polarized beamslightly lower that those for the p-polarized light.The measured deviation between the refractive in-dices for the orthogonal polarizations just exceeded,however, the error of the measurement. Future in-vestigations are needed to clarify this issue.

5. Refractive Index of Pure bR

The refractive index of pure bR is calculated from themeasured refractive indices of the bR suspensions

and from the determined four-term Sellmeier equa-tion of the TRIS buffer [Eq. (5), k ¼ 2]. The valuesobtained from the use of the accurate Schwers-formEq. (1) as well as from the approximative linearapproximation Eq. (2) are displayed in Figs. 6 and 7,respectively.

Once the refractive indices have been determinedfor the entire visible–near infrared spectral range, itis desirable to create a well-matching dispersionequation. Since the dark-adapted bR has an absorp-tion line around 560nm, a traditional Sellmeier-type formula [such as Eq. (5)] cannot be applied di-rectly. Thus, among various formulas, we preferredthe semi-empirical modification of the two-termSellmeier-type equation, resulting in the form of

nðλÞ2 − 1 ¼ A0

1þ ðλ−2 − λ−20 Þ þX2

i¼1

Ai

λ−2 − λ−2i; ð6Þ

where the fitting parameters A0 and λ0 are now re-lated to the absorption strength and position. Table 2summarizes all the coefficients of Eq. (6) for both eva-luations. It is remarkable in both cases that the cor-responding fitting procedure provided the literaryvalue of the absorption line for λ0 (see also the insetof Fig. 7). Moreover, the standard deviation of the dif-ference between the measured and fitted values(Fig. 8) was less than 0.001. As can be seen, thereis practically no difference between the accuracy ofthe Schwers form and the linear approximation.

The refractive index of pure bR, we determined, issubstantially different from that of dried bR. Thereason for this is that a cell contains a relativelylarge amount of water, which remains in the cell even

Fig. 7. (Color online) Refractive index of pure bR obtained withthe use of linear approximation (symbols) and the correspondingsemi-empirical Sellmeier fit (solid line). The values and the fit areexaggerated in the inset.

Fig. 8. (Color online) Difference between the fitted Sellmeier andthe measured values for both approximations.

Table 2. Coefficients of the Semiempirical Sellmeier Equation of Pure bR Suspension at Ambient Pressure andT ¼ 22 °C for Two- and Four-Parameter Fitting

bR Suspension A0ð1011Þ λ0 ½nm� A1ð104Þ A2ð108Þ λ1 ½nm� λ2 ½nm� ð103ÞSchwers form 6.838 559.8099 2.40692062 8.1543917 58.928371 1445.266549Linear approx. 6.838 559.8099 2.42382645 7.5111726 58.540103 1012.51599


after the preparation of the sample. Indeed, the re-fractive index of the bR is close to the refractive indexof distilled water [30].

6. Conclusion

In summary, we have measured the refractive in-dices of TRIS buffer and then the concentrationdependent refractive index of pure bRWT. We deter-mined the corresponding Sellmeier-type dispersionequations for both materials. The accuracy of themeasurement lies below 0.0004, while the error ofthe fitted dispersion equations is around 0.0001 forTRIS and less than 0.001 for bRWT. We believe thatour data set, provided for the entire visible and nearinfrared region, would be of high interest to the com-munity dealing with biophotonical applications ofbacteriorhodopsin.

The authors thank G. Groma from the Institute ofBiophysics, Biological Research Center, Szeged,Hungary, for providing the bR samples. This workwas supported by Országos Tudományos KutatásiAlapprogramok (OTKA) under grant K75149.

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refractive index of dark-adapted bacteriorhodopsin and tris(hydroxymethyl)aminomethane buffer...

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