J. Phys. Chem. 1992, 96, 7788-7792
7788
Spectral Relationship of Light-Induced Refractive Index and Absorption Changes in Bacteriorhodopsin Films Containing Wildtype BRm and the Variant BRMN
D.Zeisel and N.Hampp* Institute for Physical Chemistry, University of Munich, Sophienstrasse 11, 0-8000 Miinchen 2, Germany (Received: February 3, 1992; Zn Final Form: April 23, 1992)
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Bacteriorhodopsin films containing the variant BR", which differs from the wildtype BRW by a single amino acid exchange, Asp 96 Asn, show significantly higher holographic diffraction efficiencies (7) than BRw films. The light-induced changes of both the absorption a(A,Z) and the refractive index n(A,Z), which influence the diffraction efficiency q(A,Z), have been investigated, and their spectral dependence has been measured in order to analyze both parameters separately. A maximal change of the refractive index of An = 0.008 at 633 nm related to a modulation of the absorption of 0.55 OD, induced by actinic light of the wavelength 568 nm and an intensity of 20 mW/cm2, was observed for a BR film containing BRMN at pH 9.5. From steady-state difference spectra of the absorption, the spectral refractive index change was calculated by the Kramers-Kronig relation, and a good correlation of the theoretically derived and experimentally measured values of the refractive index changes was found. This indicates that the chromophore system of bacteriorhodopsin, which is formed by the retinal molecule, its Schiff base linkage to the protein moiety, and an inner shell of amino acids, behaves like an almost undisturbed chromophore with respect to the photorefractive properties at low actinic light intensities, despite the fact that all components of the chromophoric system are covalently linked to the amino acid matrix. Further, it was demonstrated that it is possible to calculate the spectral dependence of the diffraction efficiency q(A,Z) from the easily accessible absorption changes Aa(A,Z)and the refractive index change An(A,Z) measured at a single wavelength. This method will be a useful tool for the characterization and optimization of bacteriorhodopsin films.
Introduction During the last 2 decades, the biochemical and biophysical knowledge on bacteriorhodopsin (BR) has increased to a level where a modification of this biological photochrome in order to obtain new materials with optical properties has become The availability of BR variants has given new impulse to the field of optical applicationsof BR.536 In particular, the variant BR", which differs from the wildtype BRwT by a single amino acid exchange, aspartic acid 96 asparagine, exhibited significantly improved holographic pr~perties.~,' Many experimental studies on the light-induced absorption changes have been made in order to analyze the photocycle of BR. They cover a wide time scale down to the femtosecond range.8-'0 Apart from these investigations, a few studies have been made to analyze the time-resolved changes of the refractive index of BR during the photocycle.".'* Further theoretical investigations of the relationship between the changes of the absorption and the refractive index and the resulting holographic diffraction efficiency have been rcported.l3 For the optimization of recording media containing BR for holographic applications, a combined measurement of both parameters, the light-indud changes of the absorption Au(XJ) and the refractive index An(A,Z), is necessary to determine the wavelength ranges where maximal diffraction efficiency q( A,I) can be achieved. Due to the nonlinear optical behavior of BR, extrapolations are difficult to make from measurements which assume low substrate conversion to the optimal situation where a maximal modulation of the population distribution inside the BR film and the related modulations of a(AJ) and n(AJ) between the dark and bright regions of an incident interference pattern is desired. In this paper, we describe a modified Michelson interferometer, which was used to measure the parameters An(A,I) and Au(A,Z) and their spectral dependencies simultaneously. Further, it is shown that the spectral dependence of the absorption and of the refractive index changes can be described by Kramers-Kronig relation. This allows the calculation of the spectral dependence of the diffraction efficiency q ( A , I ) from the absorption changes Aa(AJ) and a measurement of the refractive index change An(AJ) at a single wavelength A.
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Theoretical Model The photochromic retinal protein BR consists of 7 a helices formed from 248 amino acids and a retinal molecule which is 0022-3654/92/2096-7788$03.00/0
covalently attached to bacterioopsin via a Schiff base linkage to lysine 216. In the halobacterial cell, BR acts as a light-driven proton pump. A model of the BR photocycle which summarizes the knowledge on the photochemical and thermal conversions of BR at room temperature was presented by Varo and Lanyi.I4 Several intermediates can be spectroscopically distinguished, which are represented in Figure 1 by their common single-letter abbreviations. Their absorption maxima are given as subscripts. After initial absorption of a photon by the B state, J is formed within 500 fs. From there, BR relaxes through a sequence of thermal steps to the MI state within 50 ~.tsand undergoes a nonreversible step to the MI1 state. BR then relaxes through two intermediates to the initial B state on a millisecond time scale. The M states contribute overproportionally to the photochromic properties of BR since they are blue-shifted from the other intermediates by about 150 nm. This is related to the reversible deprotonation of the Schiff base. The amino acid residues Asp 85 and Asp 96 act as proton acceptor (L MI) and proton donor (MI' N), respectively, for the change of the protonation state. Substitution of Asp 96 by Asn removes the internal proton donor capabilities of BR and leads to an increased M lifetime which depends on the extramolecular proton a~ai1ability.l~ Continuous illumination of films made from BR leads to an intensity-dependent steady-state population distribution between the B state and, due to their lifetimes, mainly the intermediates M, N, and 0 of the photocycle. Increasing the M lifetime results in "trapping" of material in the M state under illumination; Le., the BRD96Nmaterial can be converted to the bleached M form at essentially lower light intensities than BRw material. The absorption u(AbZA),dependent on the probing wavelength Ap and the intensity of the actinic light ZA, for a film of thickness d is given by a(AP,ZA) = [ ci(AP)ci(zA)ld (1)
-
-
c
i=B,M,N,O
where ei(Ap) is the molar absorption coefficient and ci(ZA)is the intensity-dependent concentration of the ith intermediate in the BR film. In the case where no light is incident onto the BR film, the absorption a(Ap,O)= €B(Ap)CB(O)dis observed, where CB(O) represents the concentration of BR molecules in the film; CB(O) can be derived from the initial optical density iOD570= cB(O)g(570 nm)d. The light-induced change of the absorption Aa(Ap,ZA) measured in the experiment is described by WApJA) = [ fi(hp)ACi(Z~)Id (2) i=B,M,N,O
0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 19, 1992 7709
Bacteriorhodopsin Films BRwTand BRmN
/
- msec
0.5 psec
B570
J600
j\-3 psec
/ OW0
t I- '
N560
\\
lrsec
L550
ti
1: H'
H' Asp 85
Asp 96
Figure 1. Simplified photocycle of bacteriorhodopsin.
/ -% BR-film
Figure 3. Initial (a) and shifted (b) fringe pattern after turning on the actinic light. The line profiles were taken near the boundary between a and b.
BE
M H
Laser 1
I PD
I
I
M2
Figure 2. Experimental setup of the Michelson interferometer.
Correlated to the change of the absorption Aa(ApJA),a change
of the refractive index An(Ap,IA) occurs according to 0
'
0
1 1 1
I
.,
1 1 1
IIr
l
I 1 I1 1 1
100
I
-.
.. .
200
I
I 1
I I ,
~
V
mI I I 1
300
II1m
400
..
I I, I..
.d
500
pixelnumber
where n(A,,,IA) describes the refractive index of the BR film and Ri(Ap)is the molar refraction of the ith intermediate.I5J6 Since the light-induced changes &(Addwere less than 0.01 in all cases investigated, the variation of the refractive index of the BR film with and without illumination can be neglected and the approximation n(Xp) = n(Xp,IA = 0 ) n(XP,IA # 0 ) can be used.
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Experimental Section Optical Setup. A modified Michelson interferometer operating in pump-probe mode1*was used for measuring the spectral dependence of the light-induced changes of the refractive index &(Addand the absorption Aa(ApJA) (see Figure 2). A spatially and temporally coherent beam from laser 1 (either a krypton laser for the wavelengths Xp = 406,413,468,476,482,520,530,568, 647,676, 752, and 799 nm or a HeNe laser for 633 nm) was expanded and spatially filtered (BE) in order to obtain a planecollimated beam in the interferometer which is f m e d by the cubic beam splitter (BS) and the mirrors (M1 and M2). This probe beam is linearly polarized perpendicular to the plane of the beams by a Glan-Taylor polarizer (GT). Mirror M1 is slightly tilted by a few milliradians in order to obtain a regular interference pattem with a low carrier frequency in the output. This fringe pattern is monitored by a CCD array. The BR film is placed in the M2 arm of the interferometer. Neutral density filters (ND) of an optical flatness of A/ 10 in the M1 arm (reference) of the interferometer compensate absorptive losses in the M2 arm in order to achieve optimal contrast in the output. Actinic light of the wavelength XA = 568 nm and an intensity of 20 mW/cm2 from a second krypton laser (laser 2) . is used to induce an intensity-dependentsteady-state population distribution of the BR molecules in the B, M, N, and 0 states. The related changes of the absorption Aa(Ap,lA)and the refractive index h ( A p , I A ) result in a change of the amplitude and in a shift of the interference pattem, respectively. This shift is proportional to the change of the optical pathway An(XRIA)dat the interferometer wavelength Xp. Since the thickness (a) is known, h(XP,IA) can be derived. Images of the initial and the
Figure 4. Line profiles of the initial (broken) and shifted interference patterns (solid) after retransformation is shown. The periods of the carrier frequency, G, and the induced shift, AG, are indicated.
shifted interference pattern, which is observed after the steady state is reached, were sampled with a CCD camera, digitzed by an 8-bit frame grabber with a resolution of 512 X 512 pixels and stored in a personal computer (PC) for evaluation. In principle, it is possible to derive the value of &(AdA) from the modulation of the fringe amplitude, but due to the low dynamic range of the frame grabber (8 bit, Le., 256 gray levels), the accuracy of the measurements is poor far BR filmswith high initial optical densities up to 5 OD, where changes of the absorption Aa up to 2 OD have to be analyzed. Therefore, a fixed fraction of -8% of the light transmitted through the BR film was reflected out of the light path by means of a glass plate (GP) and reflected onto a calibrated photodetector (PD). This light passes only once through the BR film, and the dynamic range of the photodetector is several orders of magnitude. Therefore, these values were used for further analysis. F'ringe Pattern Analysis
For the evaluation of the recorded initial and steady-state fringe patterns FPoand FPI (Figure 3), line profiles through the center of FPo and FPIwere derived (Figure 4) and the Fourier spectra FFPo = FFI'(FPo) and FFPl = FFT(FPI) were cal~ulated.~~ The spatial frequency vc which corresponds to the carrier frequency induced by the tilt angle between mirrors M1 and M2 did not change throughout the experiment. A shift of the interference pattern affects only the phase of the corresponding Fourier term but not its frequency. From the 512 pixels of the CCD camera, a Fourier spectrum at 256 spatial frequencies with a distance of Av was derived with respect to the discontinuities at both ends of the frame (Hanning window). A small-frequency range, v, f 2Av, was selected, and thereby the modified Fourier spectra MFPo and MFP, were obtained and dc terms, i.e., nonuniform background illumination and high-frequency noise, e.g., speckle patterns, were truncated.
7790 The Journal of Physical Chemistry, Vol. 96, No. 19, 1992
Zeisel and Hampp PH 8
t
I
I 1.0
iOD570= 5
B 0
8 0.0
g)
-1 .o
5 .-6
5
.g
-2.0
{
+d
t
a
-3 1 -3.0
400
-2.0
c 51
n
500
550 600 650 700 wavelength Inm]
750
450
5dO
550 600 650 700 wavelength lnml
750
1, ;
-7
io;
625
:'I,/
1.21 iOD 3.6 A iOD 5.0 -7
$! -8 675 725 775 wavelength [nml
-8 825 625
.
,:
5 ;:. pH 9.5
1
675 725 775 825 wavelength [nml
Figure 6. Refractive index changes An(A,I) in the red and near-IR (600-800 nm) dependent upon (a, left) the optical density at a constant pH value of 8 and (b, right) increasing pH value at a constant iOD value of iOD570= 5 and a thickness of 25 pm (A, = 568 nm and ZA = 20 mW/cm2). 1.0
i 2
-5.OJ 460
-5/, -6
E r
800
L
.->
t;
-3.0 450
.-
, L-3.0 800
Figure 5. Wavelength-dependent changcs of the refractive index An(X,Z) ( 0 )and absorption clo(X,Z) (A)for BRw and BRD96N.The thickness of the films is 25 pm, and the initial optical density for the samples is 3.2 and 3.6, respectively. Actinic light of wavelength AA = 568 nm and intensity ZA = 20 mW/cm2 was used to induce the population distribution
in the BR film.
After retransformation, the hd-paas-fdtered fringe patterns BFPo = iFFT(MFPo) and BFPl = iFFT(MFPJ were obtained. The light-induced change in the optical pathway An(Xp,lA)dcan be determined by this interferometric method as a fraction AG/G of the probe wavelength Xp. The change in the refractive index An(Xp,lA)can be derived by (4) where d is the sample thickness, Xp is the test wavelength of the interferometer, AG is the number of pixels by which the minimum of the interference pattern was shifted, and G l/vc is the period of the pattern given in pixels. The factor 2 in the denominator of eq 4 arises from the double path of the probe beam through the sample in the used Michelson interferometer setup. The accuracy of the interferometric setup and evaluation procedure used is S ( h ) = f3.3 X 10-4. Limitations arise mainly from the precision of the AG measurements (3 pixels) due to the low resolution of CCD array. The thickness tolerance of the BR films is 1 1 . 5 pm. The accuracy of the absorption measurement, i.e., Au and a, is approximately 3%.
-
Results
spcctrrl Dcpcnaeace of the Refractive Index Changes For all data shown here, BR films with a thickness of 25 pm and actinic light of wavelength AA = 568 nm and an intensity of ZA = 20 mW/cm2 were used. In Figure 5 , the measured absorption changes &(AdA) (triangles) in OD units and the changes of the refractive index AtI(Xp,ZA) (dots) are plotted for a BRwTand a BRm6N film with initial optical densities of iOD570 = 3.2 and iOD570 = 3.6, respectively. The obtained changes were measured when the steady state was reached after turning on the continuous actinic light. The spectral dependence of h(Ad,,) and &( X d , J is similar for both types of BR films. The maximal An(Xp,Z,J values are obtained near 470 and 630 nm, and the maximal
Aa(Xp,ZA) changes are observed at 410 and 570 nm. However, the amplitudes reached with the BR,,N films are about 4 times higher than those observed in the BRwr film. A linear dependence of the wavelength-dependent light-induced changes of Aa(Xp,ZA) and h(hp,ZA)was experimentally observed in the range of 1, = 3-30 mW/cm2 of actinic light of wavelength X = 568 nm. In order to compare the molecular properties of BR with synthetic chromophores, the difference in the molar refractions, p R B M ( X ) = RB(X) - RM(X), was derived from eq 3 under the assumption that the steady-state populations of the N and 0 states are small, which is a good approximation at least for BRm6N films.2oWith hCB = -hCM and the experimental data from Figure 5 , ARBM(633nm) = 3.6 X cm3*molecule-'is derived. This value is approximately 7 times larger than the maximum values found for synthetic organic photochromes like fulgides, e.g., (E)-a-2,5-dimethyl-3-(furylethylidene)succinicanhydride.21 For applications of BR films in holography, the photoinduced refractive index change h ( X p , l A ) in the red wing is particularly important, since almost no absorption changes are observed there. Therefore, for readout wavelengths in that range, no photochemistry in the BR film is induced, which would lead to a diminished contrast of the recorded grating. Due to this finding, holographic gratings recorded in a BR film can be nondestructively reconstructed with the wavelengths of diode lasers, e.g., 67G750 nm. For the wavelength range 600-800 nm, the influence of the initial optical density iOD570and the pH value was analyzed in more detail for BR" films. In Figure 6a, the refractive index changes h ( X p J A ) for BRmN films with increasing iOD570, 1.2, 3.6, and 5.0, are shown. The pH value of all films was pH = 8. A significant dependence of the AtI(XpJA) values on the iOD was found for the available wavelengths 633,647, and 676 nm. Almost no influence of the iOD is observed at 750 and 799 nm. This shows that increasing the optical densities of BRwN films at a constant pH value of pH = 8 lead to a higher modulation of the refractive index mainly for readout wavelengths of 650 n m - a n d 670 nm for emitting laser diodes. The same wavelength range was examined for films of constant initial optical density of iOD570= 5.0 but varying pH values, which affect the photocycle of BR (Figure 6b). The solid curve (pH = 8 and iODno) is common to both diagrams (Figure 6a and 6b). At a lower pH of 6.5, a significant decrease of the refractive index change &(A& in the whole wavelength range is observed. Increasing the pH to 9.5 results in a small increase of h ( X , Z ) compared to the pH = 8 film at all examined wavelengths except 799 nm. This shows that the refractive index modulation at red and near-IR wavelengths depends more on the pH of the BRD" film than on its optical density and that it increases with increasing pH. Comparison with the Kramers-Kronig Relation The chromophoric system of BR inside the cage formed from the amino acids of bacterioopsin is rather complex and consists
The Journal of Physical Chemistry, Vol. 96, No. 19, 1992 7791
Bacteriorhodopsin Films BRwTand BRD96N
be predicted, b a d only on experimental data, and is independent of a mathematical model of the photocycle of BR, which is still under investigation and discussion.
u
I
400
450
5;)O
550
600
650
wavelength [nml
160
7kO
%do
Spectral Dependence of the Holographic Diffraction Efficiency The spectral dependence of the diffraction efficiency q(A,Z) of thick holographic transmission gratings of thickness d on the modulation amplitudes of the refractive index nl and the absorption aid, as well as the average absorption aod in the grating, was derived by Kogelnik2' 9 = 9(%,~l,nlrd,Ap,IA) = (sin2 P + sinhZA) exp(-2D)
Figure 7. Comparison of the measured refractive index changes ( 0 )and the numerically calculated theoretical values (solid line), derived by means of the Kramers-Kronig relation for the BR" film of Figure 5. 0*025
1 where Xp is the probe wavelength and OP is the angle of incidence of the probe beam. From the data for Aa(Xp,ZA) in OD units and h ( 4 7 6 nm, 1,) measured in the experiment, the values appearing in eq 5 can be derived by means of the Kramers-Kronig relation, which produces the unscaled values Rl(XP), and a normalization to the nl value at the wavelength 476 nm
400
450
500
550
600
650
700
750
800
850
wavelength in [nml
Figure 8. Comparison of the calculated (0)and experimentally determined values (A)for the wavelength dependence of the diffraction efficiency q(X,l) of a BRWN film (iOD5,,, = 3.6 and pH = 8), where the hologram was recorded with X = 568 nm at an intensity of 5 mW/cm2 per beam.
of a retinal molecule, the reversibly protonated Schiff base linkage to the protein moiety, and a set of amino acid residues.22 Therefore, the influence of interactionsof the chromophoric system with the matrix formed by the protein on the refractive index and its spectral dependence must be carefully considered, since there is no defined border between matrix and chromophore. In addition, "long-range" effects due to the dense packing of PM patches in the films or thermal effects might occur. The measured refractive index changes An(XpJA) were compared with numerical data derived from the experimentallyobserved absorption changes Aa(Xp,IA) by means of the Kramers-Kronig relation. It was assumed that outside the analyzed visible spectral range, no absorption changes occur during the photocycle of BR. The measured changes of the refractive index h ( X P , l A ) (dots) of the BRMbN film analyzed in Figure 5 and the spectral dependence of the calculated refractive index change are plotted in Figure 7. Since the difference absorption spectrum only in the range 406-799 nm goes into the numerical analysis, the resulting absolute values for h ( X p , Z A ) are less sisnifcant than their spectral dependence. Therefore, the data were normalized to the experimentally measured h(Xp,ZA) value at 476 nm. Due to the available emission wavelengths of the krypton lasers, this value seems to be the most reliable one, since the two closely neighboring wavelengths, 468 and 482 nm, serve as a support. The spectral dependence of the measured and calculated values is almost identical. This demonstrates that no major chromophorematrix effects influencing the refractive index occur despite the fact that all parts of the chromophore, i.e., the retinyl group as well as the involved amino acids, are covalently attached to the amino acid matrix. Therefore, the chromophoric system of BR in its amino acid cage can be considered as an almost undisturbed chromophore with respect to the photorefractive properties in the investigated intensity range. For further investigations on BR films, a qualitatively correct description of the spectral dependence of the refractive index changes can be derived from the experimentally easily accessible absorption changes and the measured change of the refractive index for one selected wavelength. From these data, the spectral dependence of the holographic diffraction efficiency q( X,I) can
The factors 2.303 and arise from the conversion of decadic and natural logarithms involved in the deduction of the introduced formulas and the use of intensity and electric field-dependent descriptions. A holographic grating recorded with AA = 568 nm can be optimally reconstructed when the readout beam of wavelength Xp incidents at the Bragg angle, Le., ep = arcsin (Xp/XA sin e!). In the investigated spectral range of 400-800 nm, cos eP varies maximally from 1.O to 0.97. Therefore, for the numerical calculation of the spectral dependence of the diffraction efficiency v(Xp), the approximation cos Bp = 1 was used. The data measured for aa(XdA)and h(476,ZA)for a BRMN film of iOD570= 4.0 (see Figure 5) were used to calculate the spectral dependence of the diffraction efficiency q(XdA) according to eqs 5 and 6. The experimental v(Ap,ZA) values were analyzed with expanded beams at a light intensity of 5 mW/cmz per beam at 568 nm and a recording angle of 2flA = 20 deg. In this case, the peak intensity in the holographic grating is 20 mW/cm2 and the obtained Aa(X,Z) and h ( X , Z ) values induced are identical to those measured in the Michelson interferometer. In Figure 8, the numerical data (circles) and the experimentally measured values (triangles) are shown. Their spectral correlation is acceptable, however, in the range of the absorption band of the B state (520,530, and 570 nm); the measured values are higher than those predicted. Outside the main absorption band, especially in the red wing of the spectrum, the correlation of numerical and experimental data is good enough that this method can be used as a tool for the characterization and the optimization of BR films. The maxima for the diffraction efficiency q(X,I) are found at the predicted wavelengths, Le., 647 and 468 nm. Also, the measured values for Aa(Xp,ZA) and h(XdA) can be used directly to calculate the diffraction efficiency. In Table I, the obtained numerical and experimental data are summarized for the BR film with iOD570= 5.0 and pH = 9.5 from Figure 6 at the wavelengths 633,647,676, and 752 nm. The high modulation of the refractive index of up to 0.008 at 633 nm results in a diffraction efficiency of several percent in the red-wavelength
J. Phys. Chem. 1992, 96, 7792-1796
7792
BR films, a reliable prediction of q(XJ) and a qualitatively correct estimation of the absolute diffraction efficiency can be derived from a difference spectrum and a single measured value of the refractive index change.
TABLE I: Comparison of Calculated 8nd Measured Diffraction Efflcieneies in the Wavelength Rmge 633752 nm for a BRmN Film’ A, nm
633 647 676
752
~theol,
%
0.57 6.06 t 0.91 4.07 0.94 1.07 f 0.46 3.83
1.m %
3.40 4.70 3.51 0.85
Acknowledgmenr. We thank D. Oesterhelt and Ch. Brtiuchle for fruitful discussions. We acknowledge the financial support by the “Bundesministerium fur Forschung und Technologie”.
‘‘iODS7,, = 5.0 and pH = 9.5 for a hologram recorded at an intensity of 5 mW/cm2 per beam at 568 nm.
References and Notes (1) Oesterhelt D.; Krippahl, G. Ann. Inst. PasreurlMicrobiol. 1983, 1348,
range. All experimental data are about 20% lower than those numerically derived, but the spectral dependence is correctly predicted and a maximal diffraction efficiency of 4.7% is found at 647 nm.
137-1 50. (2) Dunn, R. J.; Hackett, N. R.; McCoy, J. M.; Chao, B. M.; Kimura, K.; Khorana, H. G. J. Biol. Chem. 1987, 262, 9246-9254. (3) Soppa, J.; Otomo, J.; Straub, J.; Tittor, J.; Mccoen, S.;Oesterhelt, D. J. Biol. Chem. 1989, 264, 13049-13056. (4) Birge, R. R. Annu. Rev. Phys. Chem. 1990.41, 683-733. ( 5 ) Hampp, N.; Briuchle, C.; Oesterhelt, D. Biophys. J . 1989,58,83-93. (6) Briuchle, C.; Hampp, N.; Oesterhelt, D. Adu. Mater. 1991, 3,
Summary and Conclusion In this paper, the simultaneous measurement of the spectral dependence of the light-induced absorption and refractive index changes at high substrate conversion rates is described for BR films containing BRwT and BRD96N.The extended M lifetime of the BRD96Nmaterial is the main reason for the observed, approximately 4 times higher, amplitudes for the changes of both the absorption and the refractive index in the whole wavelength range of 400-800 nm. The spectral dependence of both values is identical for BRw and BRD96N.The maximal refractive index change of 0.008 was observed for a BR” film of iODST0= 5.0, pH = 9.5, and a thickness of 25 pm at 633 nm at an intensity of 20 mW/cm2 of actinic light of 568 nm. It was shown that the spectral dependence of the refractive index is in good agreement with the values derived from the spectral absorption changes by the Kramers-Kronig relation. This demonstrates that no major chromophore-matrix interactions occur which influence the refractive index change. The retinal-containing chromophore of BR in its amino acid cage can be treated in a first approximation as an almost undisturbed chromophoric group with respect to the photorefractive properties in the investigated intensity range. The spectral dependence of the holographic diffraction efficiency Q( XJ) is in close agreement with the values calculated by Kogelnik’s formula. For the further characterization and optimization of
420-428.
(7) Hampp, N.; Thoma, R.; Briuchle, C.; Oesterhelt, D. Appl. Opr. 1992, 31, 1834. ( 8 ) Nuss,M. C.; Zinth, W.; Kaiser, W.; KBlling, E.; Oesterhelt, D. Chem. Phys. Letr. 1985, 117, 1-7. (9) Birge, R. R.; Findsen, L. A.; Pierce, B. M. J . Am. Chem. SOC.1987, 209. 5041-5043. (10) Mathies, R. A.; Cruz, C. H. B.; Pollard, W.T.; Shank, C. V. Science 1988, 240, 777-779. (11) Savransky, V. V.; Tkachenko. N. V.: Chukarev. V. I. Biol. Membr. 1987, 4,479-485: (12) Tkachenko, N. V.; Savransky, V. V.; Sharonov, A. Y. Eur. Biophys. J. 1989, 17, 131-136. (13) Birge, R. R.; Izgi, K. C.;Stuart, J. A.;Tallent, J. R.Proc. Mar. Res. SOC.1991, 218, 131-140. (14) Varo, G.; Lanyi, J. K. Biochemistry 1991. 30, 5008-5015. (15) Tomlinson, J. W.;Chandross, E. A.; Fork, R. L.; Pryde, C. A.; Lamola, A. A. Appl. Opt. 1972, 11, 533-548. (16) Burland, D. M.; Briuchle, Ch. J . Chem. Phys. 1982,76,4502-4512. (17) Miller, A.; Oesterhelt, D. Biochim. Biophys. Acra 1990,1020,57-64. (18) Cotter, D.; Ironside, C. M.; Ainslie, B. J.; Girdlestone, H. D. Opr. Lett. 1989, 14, 317-319. (19) Takeda, M.; Ina, H.; Kobayashi, S. J . Opr. Soc. Am. 1983,72, 156. (20) Hampp, N.; Popp, A.; Briuchle, C.; Oesterhelt, D. J . Phys. Chem. 1992, 96, 4679. (21) Kirkby, C. J. G.; Cush, R.; Bennion, I. Opr. Commun. 1985,56,288. (22) Fischer, U.; Oesterhelt, D. Biophys. J . 1979, 28, 21 1-230. (23) Kogelnik, H. Bell Sysr. Tech. J . 1969, 48, 2909.
Enthalpy of Knotted Polypeptides Teresa Head-Gordon* and Frank H. Stillinger AT&T Bell Laboratories, Murray Hill, New Jersey 07974 (Received: April 13, 1992)
This paper concerns the estimation of the enthalpy of knotted conformers of poly-L-alanine, using a molecular mechanics force field. We have evaluated the relative energies of a variety of conformers of poly-L-alanine, including knots, for the size regimes of 58 and 124 residues. The knots investigated include right- and left-handed knots, knots containing helical secondary structure, supersecondary structure knots formed by turns in a helix to fold the helical backbone into a knot, and knots of varying degrees of tightness. While often the entropic barrier is cited for lack of observed knots in existing protein native structures, we find that the enthalpic barrier to knot formation is at least as formidable, -100-350 kcal/mol for poly-L-alanine, a barrier which will likely be larger when considering most native sequences.
Introduction One striking observation concerning protein native conformations is that well-defined knotted structures do not occur in the current database of crystallized proteins. Our definition of a knot is the shoelace tie of the polypeptide backbone and not knots which result from threading through loops formed by covalent disulfide bonds.’J One protein, carbonic anhydrase: shows the last residue’s carboxyl end just barely threading through a backbone loop region;
if the ends of the carbonic anhydrase polypeptide chain were pulled in opposite directions, a knot would result? However, this is a marginal and exceptional case which in our view does not qualify as a genuine knotted structure. Why are there no knotted proteins? One plausible reason is that a large entropic barrier makes it highly improbable for a knotted fold to occur. From this perspective it has been suggesteds that the observed (unknotted) native structure is a kinetically
0022-365419212096-7792$03.00/00 1992 American Chemical Society
