J. Phys. Chem. B 2002, 106, 6303-6309
6303
Membrane Proteins in Bulk Solution Can Be Used for Quasi-Elastic Neutron Scattering Studies: The Case for the Photochemical Reaction Center Andrew Gall,*,† Je´ roˆ me Seguin,‡ Bruno Robert,‡ and Marie-Claire Bellissent-Funel† Laboratoire Le´ on Brillouin (CEA-CNRS), CEA-Saclay, 91191 Gif-sur-YVette Cedex, France, and SerVice de Biophysique des Fonctions Membranaires, DBJC/CEA and URA CNRS 2096, CEA-Saclay, 91191 Gif-sur-YVette Cedex, France ReceiVed: NoVember 8, 2001; In Final Form: March 19, 2002
The potential to measure the internal dynamics of a membrane protein, the bacterial photochemical reaction center (RC) from the photosynthetic bacterium Rhodobacter sphaeroides, was investigated by incoherent quasi-elastic neutron scattering (IQENS) and neutron spin-echo spectroscopy. To isolate and maximize the scattering intensity attributed to the protein, selective deuteration was employed. This deuteration was achieved by embedding detergent-purified RC proteins in a solution containing perdeuterated D28-n-octyl-β-Dglucopyranoside, a sugar-hydroxy detergent. Therefore, the IQENS signal essentially arises only from the motions, which are resolved in time, of the nonexchangeable hydrogen atoms of the protein. This work has established that with a suitable biochemical protocol detailed measurements on the internal dynamics of any integral membrane protein can be undertaken.
Introduction Recently, there has been an explosion in the number of studies of globular protein dynamics as a function of hydration, temperature, and structure, namely, native versus denatured or molten globule,1-11 as measured by incoherent quasi-elastic neutron scattering (IQENS) spectroscopy combined with the concept of isotopic contrast variation.12 IQENS is sensitive mainly to the motions of nonexchangeable hydrogen atoms, which are located quasi-homogeneously in proteins. As a result, IQENS is able to monitor the averaged dynamics of this class of biological macromolecules.13,14 Pe´rez and co-workers have carried the analysis of the hydration level to small globular proteins in bulk solution.15 However, this type of study is inherently more difficult for large integral membrane proteins because they require a hydrophobic phase, such as exogenous lipid or detergent, to stabilize them.16 The requirement for a protective detergent sheath that does not denature the biological macromolecule is one of the major reasons that there are relatively few 3-D structures of membrane proteins.16,17 The elucidation of the first X-ray crystal structure of a membrane protein was that of the bacterial photochemical reaction center (RC) from Rhodopseudomonas (Rps.) Viridis.18,19 This structure has been followed by a number of RC structures from the related bacterium Rhodobacter (Rb.) sphaeroides, with resolutions up to 2.1 Å.20-23 The ca. 100 kDa RC is part of the bacterial photosynthetic apparatus, which also consists of one or a few types of light-harvesting (LH) complexes forming a network of interconnecting proteins localized in the intracytoplasmic membrane.24,25 Photons are first absorbed by the noncovalently bound bacteriochlorophyll (Bchl) and carotenoid chromophores in the LH antennae, and the resulting excitation energy is transferred to the RC. Subsequent electron transfer within the RC produces a chemical potential gradient across the membrane.26 *Corresponding author. E-mail:
[email protected]. Tel: 33-01-69 08 97 01. Fax: 33-01-69 08 82 61. † Laboratoire Le ´ on Brillouin (CEA-CNRS), CEA-Saclay. ‡ Service de Biophysique des Fonctions Membranaires, CEA-Saclay.
In the X-ray crystal structure from Rb. sphaeroides, strain R26.1, the RC consists of two multiple transmembrane polypeptides, L and M, with very similar tertiary conformations arranged in pseudo-C2 symmetry. Each polypeptide consists of five membrane-spanning helices that are linked by a series of small helices and loop regions. These 10 large helices form a cage that encases the hydrophobic chromophores. The third polypeptide, H, is much less hydrophobic, and it contains only a single membrane-spanning helix located at the N terminal of its sequence. The majority of this polypeptide is located at the membrane interface on the cytoplasmic side of the membrane. A comprehensive review of the structure and function of the RC can be found in ref 20. Located throughout the volume of the hydrophobic L-M cage are individual chromophores that constitute a series of internal molecular probes: these consist of a pair of excitonically coupled Bchl molecules that constitute the primary donor (P), two monomeric accessory Bchl molecules, and two bacteriopheophytin a (Bpheo) molecules. The interactions between the chromophores and their protein environments yield information on the structure of the photochemical RC and how it responds to external stress. The X-ray crystal structures of the various RCs were determined from detergent-isolated proteins. The detergent ring that protects the hydrophobic transmembrane region from the bulk solvent has been visualized using neutron diffraction spectroscopy combined with the concept of isotopic contrast variation.27,28 In Rb. sphaeroides, the detergent used in the crystallization experiments and subsequent neutron diffraction experiments was n-octyl-β-D-glucopyranoside (βOG).28 The neutron diffraction studies have shown that for a solution suitable for crystallization there are approximately 205 βOG molecules surrounding each Rb. sphaeroides RC.28 Related biochemical studies have shown that in the standard βOG solution of 10 mM TrisCl, pH 8.0, there are on average 360 detergent molecules per RC protein.29 There are a number of cases where the function-structure relationship of the purple membrane from the bacterium Halobacterium salinarum, which mainly contains the 26-kDa
10.1021/jp014079l CCC: $22.00 © 2002 American Chemical Society Published on Web 05/25/2002
6304 J. Phys. Chem. B, Vol. 106, No. 24, 2002 protein bacteriorhodopsin, has been investigated by incoherent quasi-elastic neutron spectroscopy. To date, this system has been used as the prototype model for membrane proteins.30,31 In this work, we have employed the principle of isotopic labeling to minimize the scattering intensity arising from the RC-bound detergent and bulk solution during incoherent quasi-elastic neutron scattering events for the standard RC solution.29 This minimization has been achieved by incubating hydrogenated Rb. sphaeroides RC proteins, where the labile hydrogen atoms have been previously exchanged, in a perdeuterated detergentbuffer environment. The resulting incoherent neutron scattering intensity essentially arises only from the motions, which are resolved in time, of the nonexchangeable hydrogen atoms of the integral membrane protein, thus opening the door to the development and study of other membrane systems with known X-ray crystallographic structures. Methods and Materials Cell Culturing, Membrane Isolation, and Protein Purification. Rb. sphaeroides, strain R26.1, was cultured photosynthetically at 28 °C in Bo¨se medium;32 membranes were prepared and solubilized on the basis of previously described methods.33,34 Washed membranes were diluted to an A800 value of 50 with Tris buffer (20 mM TrisHCl, pH 8.0) and then solubilized with 15.3 mM N,N-dimethyldodecylamine-N-oxide (LDAO) for 90 min at 26 °C, followed by 3-fold dilution with Tris buffer. Following a low-speed centrifugation step (10k × g, 10 min) to remove any unsolubilized debris, the RC complexes were isolated by high-speed centrifugation (250k × g, 70 min). The RC-containing supernatant was loaded onto a preequilibrated anion exchange column (4.4 mM LDAO, 20 mM TrisHCl, pH 8.0, DEAE 650s, Fractogel, TosoHaas, Montgomeryville, PA). After a salt gradient was applied (10-400 mM NaCl), the spectroscopically pure fractions were concentrated (Centriprep30, Amicon, Bedford, MA) and loaded onto a preequilibrated size-exclusion column (3.3 mM LDAO, 50 mM NaCl, 10 mM TrisHCl, pH 8.0 Fractogel TSK HW-55, TosoHaas, Montgomeryville, PA). Finally, the purified pigment-protein complexes were subjected to a second anion exchange column (Resource Q, Pharmacia, Uppsala, Sweden). The polypeptide composition of the purified RC complexes was verified by SDSpolyacrylamide gel electrophoresis, as described in ref 35. The SDS-PAGE gels were developed using the Silver Stain Plus kit (Bio-Rad Laboratories, Hercules, Ca). Electronic absorption spectra were recorded using a Cary 5E (Varion, Sydney, Australia) double-beam spectrophotometer to verify the electronic absorption properties of the proteins. All spectroscopic measurements were carried out at 288 K. Deuterium Exchange. The reagents that constitute the Tris buffer were replaced by deuterium-labeled compounds by repeated washings with 3.3 mM LDAO, 20 mM D11-Tris (D11Tris, Isotopchim, Ganagobie-Peyruis, France) in D2O (EurisoTop, Gif-sur-Yvette, France), pD 7.6, using Centricon 30 concentrators (Amicon, Bedford, MA) followed by extensive dialysis at 281 K. The detergent LDAO was then exchanged for βOG (BioMol, Hamburg, Germany) using proven techniques,36 giving a final detergent concentration of 28 mM. After dialysis (3 days with 6 changes of dialysis buffer), the detergent was exchanged for D28-βOG (Cambridge Isotopes, MA) as described above, giving a final D28-βOG/βOG ratio in excess of 95% in a completely predeuterated buffer solution. This procedure was followed by 39 days of dialysis to ensure that the maximum possible H/D37 and detergent exchange had occurred between the bulk solution and the protein micelles.
Gall et al. After final verification of protein integrity, the hydrogendeuterium-exchanged protein in its detergent microemulsion was prepared for elastic and inelastic neutron scattering measurements. Incoherent Quasi-Elastic (IQENS) and Inelastic Neutron Scattering. In-depth descriptions of general quasi-elastic neutron scattering13 dry versus hydrated protein dynamics14 and the internal dynamics of proteins in solution15 have been previously reported. Here, we shall remind the reader of the basic principles behind incoherent quasi-elastic neutron scattering that are applicable to biological macromolecules. The transfer of energy, pω, and momentum, pQ, are related to the time correlation functions of the atomic motions of the molecules that constitute the sample. The scattering vector, Q B , is related to the neutron initial and final wavevectors by the equation pQ B ) pk B - pk B0 where k0 and k are the corresponding wavevector moduli, m is the neutron mass, and p is the Planck constant divided by 2π. The energy transfer, pω, between the initial, Eo, and final, E, energies of the neutron is described by the relation
pω ) E - E0 ) p2/ 2m(k2 - k 20)
(1)
During a neutron scattering experiment, we measure the double differential scattering cross section, d2(σ)/(dΩdω), which provides information on energy transfer and neutron scattering distribution for a solid angle, dΩ.12 The total neutron scattering cross section, σ, comprises two parts, namely, the isotopicspecific coherent neutron scattering cross section (σcoh) and the incoherent neutron scattering cross section (σinc):
d2σ/dΩdω ) (d2σ/dΩdω)coh + (d2σ/dΩdω)inc
(2)
In incoherent quasi-elastic neutron scattering experiments, we measure the neutron scattering intensity as expressed by the relation
d2σ/dΩdω )
k σinc S (Q, ω) N k0 4π inc
(3)
where N is the number of nuclei and Sinc(Q, ω) is the selfdynamic structure factor. Sinc(Q, ω) can be decomposed into separate elastic, quasi-elastic, and inelastic components
Sinc(Q, ω) ) Selas(Q, ω ) 0) + Squasi(Q, ω) + Sinelasc(Q, ω) (4) where the elastic peak originates from neutrons undergoing no change in energy. The quasi-elastic line is attributed to the diffusive, rotational, or translational motions and consists of a broad band of intensity centered at ω ) 0. The inelastic component, Sinc(Q, ω), is related to the vibrational modes of the sample and to real-space dynamics by the formalism developed by van Hove.38 A neutron scattering event is deeply dependent on the atomic properties of the scattering nucleus. The hydrogen nucleus has a very large incoherent (σinc) neutron scattering cross section of 80.26 barn when compared to that of the other common nuclei found in proteins: σinc(D) ) 2.05 barn, σinc(C) < 0.01 barn, σinc(N) ) 0.49 barn, σinc(O) < 0.01 barn, σinc(P) < 0.01 barn, σinc(S) < 0.01 barn. During an IQENS experiment, because the incoherent neutron scattering cross section of hydrogen dominates, we essentially measure only the incoherent scattering events of hydrogen (see eq 2). Moreover, because H nuclei are located quasi-homogeneously throughout the volume of a protein, we measure the averaged motions of the entire
RC Dynamics
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biological macromolecule within the temporal domain set by the spectrometer. Global and Internal Motions for a Protein in Solution. In solution, the total scattering function Sinc(Q, ω)of the protein can be expressed as
Sinc(Q, ω) ) l(Q, ω) X Sinternal(Q, ω)
(5)
where the global Brownian motions, l(Q, ω), are convoluted by internal motions, Sinternal(Q, ω), of the macromolecule;15 X is the energy convolution operator. Using this methodology, the global motions of the protein are removed from the spectrum, and Sinternal(Q, ω) values are obtained. Experimentally, the resolution of the apparatus and residual contributions from vibrational large-scale modes must also be taken into account. Therefore, in the quasi-elastic region, the experimental data is fitted by the relationship
Sinc,exp(Q, ω) ) P(Q) e-pw/2kBT [Sinternal(Q, ω) + B(Q)] X Sres(Q, ω) (6) where P(Q) ) e-〈µ2〉Q2/3 if the coherent signal is ignored.13 The function B(Q) accounts for the remaining contribution from the large-scale vibrational modes and has a Q2 dependency in the quasi-elastic region; Sres(Q, ω) is the experimental resolution of the apparatus and is obtained from the scattering properties of the totally elastic incoherent vanadium sample. The standard IQENS fitting programs at the Laboratoire Le´on Brillouin (LLB) were used to obtain the experimentally derived parameters that are described below. Solvent Subtraction. First, the buffer and protein spectra were normalized to the same incident neutron intensity. The scattering function ascribed to the protein was derived using the equation
Sprotein(Q, ω) ) Sprotein/buffer(Q, ω) - (1 - V) × Sbuffer(Q, ω) (7) where V corresponds to the volume occupied by the proteins in the sample holder. The volume occupied by each RC-βOG micelle has been shown to be 225 000 Å3.28 The RC concentration (c) in the sample was calculated to be 97.9 µM using the RC Beer-Lambert relationship Aλ) λcl where λ)802nm ) 288 -1 -1 mM cm and l is the path length (cm). The volume occupancy of the RC-βOG, namely, the protein/buffer, structures consists of 1.3% of the total volume in the sample cell. Time of Flight. IQENS measurements were performed using the high-resolution time-of-flight spectrometer Mibe´mol (Laboratoire Le´on Brillouin, CEA-Saclay). The incident neutron wavelength was 9 Å. An experimental resolution, half-width at half-maximum (hwhm), of between 30 and 32 µeV was obtained for the wave vector range of 0.29-1.31 Å-1. A circular aluminum cell adapted for solutions was used as a sample holder. The depth of the sample holder wall was 0.5 mm, the path length of the neutron beam through the sample was 0.7 mm, and the internal radius of the sample was 25 mm. The cell was orientated 45° to the incident neutron beam. The transmission of the sample holder containing the protein solution was measured with an incident neutron wavelength of 6 Å and was found to be 0.86 (when normalized against the empty beam containing no sample holder). Neutron Spin-Echo. For a detailed synopsis of neutron spin-echo (NSE) methodology, see ref 39 and references therein. In summary, the final polarization of the scattered neutrons, P(Q, H), is measured as a function of the applied
magnetic field, H. The magnetic field is converted to a time variable by a Larmor precession equation resulting in a window of time measurements. P(Q, H) is proportional to the real part of the intermediate scattering function where I(Q, t) is the signal intensity at time, t:
I(Q, t) ∝
∫ cos(ωt) S(Q, ω) dω
(8)
If the dynamic structure factor, S(Q, ω), has a Lorentzian shape, then its Fourier transform, I(Q, t), can be expressed as an exponential decay, exp(-t/τ), where 1/τ ) DappQ2. Dapp is the apparent diffusion coefficient. The inelastic neutron spin-echo spectrometer Mess (Laboratoire Le´on Brillouin, CEA-Saclay) was used to measure the diffusive motions of the sample at 288 K for a Q range between 0.027 and 0.153 Å-1. The incident neutron wavelengths were 5 and 6 Å (hwhm ≈ 9.5%). Graphite was used to establish the resolution of the spectrometer and to normalize the measured sample intensities. Small Angle Neutron Scattering. The small angle neutron scattering (SANS) experiments were performed at 288 K with the spectrometer Paxe (Laboratoire Le´on Brillouin, CEA-Saclay) in quartz cells (Quartz Suprasil, Hellma). The neutron wavelength was 10 Å, and the sample-to-detector distance was 2.1 m, giving a scattering vector, Q, range between 6.1 × 10-3 and 6.5 × 10-2 Å-1. The buffer-subtracted SANS spectra of the protein were obtained using previously described methods.40,41 For values of Q that are sufficiently small, the Guinier approximation may provide information about the size of the object. The normalized SANS spectrum was modeled as a solid sphere using the Guinier approximation,42 which may be written as
LnI(Q) ) LnI(0) - (Q2R 2g )/3
(9)
where I(0) is the forward-scattered intensity and Rg is the apparent radius of gyration of the object. In a Guinier plot (Ln(I) vs Q2), the slope of a straight line through the data equals x3Rg.42 Quasi-Elastic Light Scattering. Quasi-elastic light scattering measurements (QELS) were performed at 288 K on a diluted protein solution with an apparatus that has been described previously.43 An incident wavelength of 647 nm (where the chromophore molecules have the least absorbance) was provided by a krypton laser (Coherent 90), and data was collected for scattering angles between 90 and 150°. Results and Discussion The 288 K electronic absorption spectrum of the photochemical RC from Rb. sphaeroides R26.1 after preparation for neutron scattering measurements is shown in Figure 1. The absorption peaks at 760, 802, and 870 nm arise from the Qy absorption transitions of the Bpheos (HM and HL), the accessory Bchls (BM and BL), and the primary electron donor (Bchls PM and PL), respectively. The Qx electronic transitions of the Bchl and the Bpheo chromphores are at ca. 600 and ca. 535 nm, respectively. Upon deconvolution of the Qx Bpheo, we obtained two Gaussian curves that approximate the electronic absorption bands of HM and HL with absorption maxima at 530 and 543 nm, respectively (Figure 1, insert). Our absorption spectrum is identical to that of untreated RCs.44 Therefore, the absorption properties of the different chromophores (Bchls and Bpheos), which are located throughout the volume of the protein, indicate that the deutera-
6306 J. Phys. Chem. B, Vol. 106, No. 24, 2002
Gall et al. TABLE 2: Percentage Contribution to Total Number of Hydrogen and Deuterium Nuclei Per Photochemical RC in a Perdeuterated Solution structure
percentage of hydrogen nuclei
percentage of deuterium nucleia
polypeptides cofactors/chromophores detergent
86.4 7.0 6.6
10.7 0.1 89.2
a The apparent low value for the deuterium nuclei (namely the exchangeable hydrogen atoms) from the polypeptides is due to the extensively deuterated detergent sheath that encompasses the hydrophobic phase of the membrane protein.
Figure 1. Electronic absorption spectrum of the RC protein in solution after the neutron scattering experiments. Inset: expanded view of the absorption bands attributed to the two Bpheo molecules. Gaussian distributions were used to approximate the individual absorption transitions (see text).
TABLE 1: Quantification of the σinc and σcoh Values Attributed to One RC Protein and Its Protective Detergent Ringa element/isotope
σ
σcoh
H D C N O Mg S
5.06 × 8.29 × 104 5.49 × 104 1.28 × 104 1.41 × 104 1.48 × 101 2.57 × 101
1.08 × 6.07 × 104 5.49 × 104 1.22 × 104 1.41 × 104 1.45 × 101 2.55 × 101
4.96 × 105 2.22 × 104 9.89 × 100 5.55 × 102 0.00 × 100 3.20 × 10-1 1.75 × 10-1
total
6.71 × 105
1.53 × 105 (23%)
5.18 × 105 (77%)
105
104
σinc
a The values are in barns and are rounded to two decimal places. The neutron scattering profiles for each element (except H and D) are based on the averaged scattering properties resulting from the natural abundance of multiple stable isotopes.
tion process has not affected the internal structure of the bacterial photochemical RC in as far as can be judged from these properties. Prior to the actual neutron scattering experiments, the RC was checked for its suitability for data collection. The transmission of the RC protein solution (including the sample holder) was measured with an incident neutron wavelength of 6 Å with the spectrometer Mess (LLB, CEA-Saclay) and was found to have a transmission of 0.86. Therefore, multiple neutron scattering events in the sample may be neglected.13 The theoretical quantification after H/D exchange was performed on the basis of the X-ray crystal structure.27,28 We have incorporated each RC in 360 n-octyl-β-D-glucopyranoside molecules,29 95% of which are perdeuterated, in the standard βOG solution of 10 mM TrisCl. Because there is rather limited data on the kinetics of H/D exchange in integral membrane proteins and we know of none for the RC, we have assumed that all the exchangeable hydrogen atoms have the potential to be replaced by deuterium, even those nuclei deep inside the hydrophobic core. The quantification of the incoherent neutron scattering cross section (σinc) and the coherent neutron scattering cross section (σcoh) attributed to one RC protein and its protective detergent ring is presented in Table 1. Of the total neutron scattering cross section, 77% arises from σinc (518 417 barn). Furthermore, 96% of σinc (495 605 barn) is attributed to the hydrogen nuclei. As a result, the sample has sufficient incoherent neutron scattering
character to permit an IQENS experiment to be undertaken. The data were then analyzed on the basis of the different structural elements within each protein-detergent micelle. For each protein-detergent micelle, 82% of σinc and 34% of σcoh arise from the protein (polypeptides and chromophores). The relative number of exchangeable (D nuclei) and nonexchangeable (H nuclei) hydrogen atoms per RC is indicated in Table 2, where the percentage contributions from the polypeptides, the pigment cofactors, and the encompassing detergent sheath are presented. There are virtually no labile protons attributed to the pigment cofactors. The hydroxyl groups of the deuterated detergent molecules have the slight potential to be hydrogenated in a D2O/H2O solution and thus may account for a very small fraction of the overall H nuclei. At this point, we must stress that because of the extensive dialysis time neartotal deuteration is expected, and we have assumed that all the labile hydrogens from the detergent molecules are not protonated. After H/D exchange, the polypeptides account for over 86% of the H nuclei per pigment-protein micelle. Conversely, the detergent molecules account for approximately 90% of the D nuclei whereas the remaining 10% originates from the actual protein. Taking into account the difference in neutron scattering cross sections between the different nuclei, it is apparent that incoherent neutron scattering events arise mainly from the protein and more specifically from the three individual polypeptides. Prior to making the incoherent quasi-elastic neutron scattering (IQENS) and neutron spin-echo (NSE) measurements, the structure of the protein-detergent micelles was examined by small angle neutron scattering (SANS). The goal of the SANS trials was not to create an accurate 3-D model of the RC but rather to verify that the protein was not subject to extensive aggregation during H/D manipulations. For this reason, we (i) used a limited number of protein concentrations, (ii) calculated a simple radius of gyration based on a sphere, and (iii) made no attempt to match out fully the SANS signal that arises from protein-bound detergent. Shown in Figure 2 is the Guinier plot of the normalized SANS intensity from a dilute solution (7.9 µM) of our RC preparation. The radius of gyration, Rg, was calculated to be 31.8 ( 0.1 Å. Using the quantitative relationship41 between the Zimm45 and Guinier42 approximations, we determined the radius of gyration at infinite dilution, Rg(0), to be the intersect on the abscissa axis when Rg-2 is plotted as a function of protein concentration (Figure 3.). Rg(0) was found to be 31.3 ( 0.5 Å for the concentration range 0-30 µM, which suggests that the volume of our RC is 1.3 × 105 Å3 at infinite dilution and is comparable to the value (1.25 × 105 Å3) that has been derived from the X-ray crystal structures. Thus, our RC may be considered to be essentially monomeric in solution. Indeed, our experimentally determined Rg is similar to more detailed SANS experiments on a 23-µM solution of fully deuterated RCs in a hydrogenated solution (0.8% βOG in Tris-
RC Dynamics
Figure 2. Guinier plot of a dilute protein solution. The radius of gyration, Rg, is 31.8 ( 0.1 Å.
Figure 3. Determination of the radius of gyration at infinite dilution, Rg(0) ) 31.3 ( 0.5 Å. The slope of the line is slightly negative, indicating repulsive interactions between neighboring proteins.
H2O buffer) that produced an Rg(23 µM) value of 31.5 ( 0.2 Å.46 By extrapolation of the data presented here, our RC has an Rg(23 µM) of 31.9 Å, thus providing strong evidence that the detergent micelle is indeed fully deuterated. With the NSE spectrometer Mess (Laboratoire Le´on Brillouin, CEA-Saclay), the intermediate scattering function, I(Q, t), can be reliably measured for a Q range where data is generally impossible to obtain with classic time-of-flight and backscattering spectrometers. Shown in Figure 4 is I(Q, t) at Q ) 0.153 Å-1 for the photochemical RC (after buffer subtraction). The most notable feature of the data is that it can be fitted using a single exponential decay, which indicates that at this scattering vector we are in effect measuring only the diffusion constant of the whole protein. To confirm this idea, a series of NSE spectra were taken for a range of scattering vectors, and the decay rates were determined. Figure 5 shows the relationship between the reciprocal of the decay rate (1/τ) as a function of Q2. The data obeys the model for free diffusion, Γ ) DappQ2, for which the diffusion constant was calculated to be 3.6 ( 0.2 × 10-7 cm-2 s-1. As a control, the protein solution was then diluted 100-fold using the same deuterated buffer, and the diffusion constant was determined using quasi-elastic light scattering and was found to be remarkably similar at 3.7 ( 0.3 × 10-7 cm-2 s-1. In this work, under dilute conditions (relevant to electronic measurements) and concentrated conditions (relevant to IQENS
J. Phys. Chem. B, Vol. 106, No. 24, 2002 6307
Figure 4. Intermediate scattering function I(Q, t) for the scattering vector Q ) 0.15 Å-1 measured by the neutron spin-echo spectrometer Mess. The line represents a fit with a single-exponential decay, e(-t/τ), where τ ) 12 ( 0.9 ns.
Figure 5. Evolution of 1/τ as a function of Q2. The solid line is a linear fit that gives a diffusion constant of 3.6 ( 0.2 × 10-7 cm-2 s-1.
and NSE measurements), the RC proteins are monomeric, as evidenced by whole-body diffusion constants, Dapp. Therefore, quasi-elastic neutron scattering may be used to complement other spectroscopic methods. For example, resonance Raman and femtosecond coherence spectroscopy, each of which measure frequency changes in the bacteriochlorin molecules, have shown that the low-frequency mode at 30-34 cm-1 modulates during charge separation and is probably due to some periodic structural change in the polypeptides.47-49 This result is noteworthy because IQENS essentially measures the lowfrequency dynamics (
