2160
J . Phys. Chem. 1990, 94, 2 160-2 166
Theoretlcal Analysis of Resonance Raman Spectra from the Blue Copper Protein Azurin Mahfoud Belhadj, John M. Jean, Richard A. Friesner,* Department of Chemistry, University of Texas, Austin, Texas 78712
John Schoonover, and William H. Woodruff Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (Received: May 17, 1989; In Final Form: September 2, 1989)
Using a time domain methodology, we have simulated low-temperature resonance Raman data from the blue copper protein azurin in an effort to determine an effective harmonic potential surface (relative to the ground-state geometry and normal coordinates) for the 600-nm transition of the blue copper active site. We find that utilization of overtone and combination intensities greatly facilitates the extraction of reliable parameter values. We are able in this manner to obtain accurate results for the linear displacements of the excited-state surface. Quadratic parameters are more difficult to determine; however, some progress in this direction can be made.
I. Introduction In a series of previous papers, we have developed a time domain approach to the computation of resonance Raman (RR) intensities for multimode systems under the assumption of ground- and excited-state harmonic potential s ~ r f a c e s . l - ~The method has recently been applied to analyze R R data from two transitionmetal ~ o m p l e x e sin , ~which finite temperature effects and mode mixing (which are difficult to treat in other approaches) were important. These calculations demonstrated the utility of the method in the context of a small test problem. In the present work, we study R R data at low temperature from the blue copper protein azurin. The blue copper proteins are an important family of electron-transfer proteins which play a key role in metabolic functions of plants and animals. A substantial amount of quantitative spectroscopic data exists for many members of the family at both cryogenic and room temperat~re.~-lIThe analysis presented below should be regarded as a preliminary step in a thorough investigation of the entire available body of RR and absorption data. We focus here on rather different issues in the theoretical simulation of RR intensities from large, multimode systems than in ref 4. The quality of the data is not quite good enough to allow a quantitative investigation of mode mixing effects (although this state of affairs should be correctable by improving the experimental signal-to-noise ratios), and we do not discuss temperature effects. Rather, the emphasis is on the importance of using overtone and combination intensities in determining excited-state equilibrium geometry displacements and force constant alterations in a reliable manner. Previous workers have generally ignored the over( I ) Friesner, R. A.; Pettitt. B. M.; Jean, J. M . J . Cfiem.Pfiys. 1985, 82, 2918. (2) Jean, J. M.; Friesner, R. A. J . Cfiem. Pfiys. 1986, 85, 2353. (3) Jean, J. M.; Belhadj, M.; Friesner, R. A. To be submitted for publication. (4) Jean, J. M.; Belhadj, M.; Friesner, R. A.; Morris, D. E.; Woodruff, W. H. J . Am. Cfiem.Soc., in press. ( 5 ) Miskowski, V.; Tang, S.-P.; Spiro, T. G.; Shapiro, E.; Moss, T. H. Biochemistry 1975, 14, 1244. (6) Solomon, E. I.; Hare, J. W.; Gray, H. B. Proc. Natl. Acad. Sci. U.S.A. 1976, 73, 1399. (7) Siiman, 0.;Young, N . M.; Carey, P. R. J . Am. Cfiem.SOC.1975. 98, 744. (8) Solomon, E. I.; Hare, J. W.; Dooley, D. M.; Dawson, J. H.; Stephens, P. J.; Gray, H. B. J . A m . Cfiem.SOC.1980, 102, 168. (9) Woodruff, W. H.; Norton, K . A,; Swanson, B. 1.; Fry, H. A. J . Am. Cfiem.SOC.1983, 105, 657. (10) Woodruff, W. H.; Norton, K. A,; Swanson, B. I.; Fry, H. A. Proc. Nail. Acad. Sci. U.S.A. 1984, 81. 1263. (1 1) Blair, D. F.; Campbell, G. W.; Schoonover, J. R.; Chan, S. 1.; Gray, H. B.; Malmstrom, B. G.; Pecht, I.; Swanson, B. I.; Woodruff, W. H.; Cho, W. K.; English, A. M.; Fry, H, A.; Lum, V.; Norton, K . A. J . Am. Cfiem.Soc. 1985, 107, 5755.
0022-3654/90/2094-2 160$02.50/0
tone/combination (O/C) region, pursuing instead other cross checks on the results, e.g., absolute intensitie~.'~-'~It is our contention that the O/C region is straightforward both to study experimentally and to analyze theoretically and that failure to do this can, in some cases, lead to considerable uncertainty in even linear coupling excited-state parameters. On the other hand, a careful treatment of the O/C region provides sufficient overdetermination to at least obtain reliable values for the linear displacements. The calculation of accurate intensities in the O/C region is particularly simple in our system of R R and absorption simulation programs, as all orders of scattering are evaluated automatically in a single computation. However, other time domain appro ache^^^-^^ can also be used for these calculations, particularly if mode mixing and finite temperature effects are not of importance. The models employed in this paper (low temperature, no mode mixing) in fact present no problems for the majority of the approaches in the work cited above. The remainder of this paper is divided into five sections. In section I1 the experimental methods are briefly described, as well as the procedures used to determine integrated intensities from the Raman profiles. Section 111 discusses the means by which the data are converted into integrated intensities suitable for theoretical analysis and briefly reviews the theoretical methodology. The remaining two sections present the results and conclusions. We note that a number of other research groups have made extensive investigations of resonance Raman excitation profiles in proteins, often with excellent agreement between theory and e ~ p e r i m e n t . The ~ ~ ~work ~ ~ reported ~ ~ ' ~ ~here ~ should be seen as an extension of these efforts, incorporating additional constraints via the O/C region and thus hopefully allowing greater reliability in parameter determination. (12) Trulson, M. 0.; Mathies, R. A. J . Cfiem. Pfiys. 1986, 84, 2068. (13) Myers, A. B.; Harris, R. A.; Mathies, R. A. J. Cfiem.Pfiys. 1983, 79, 603. (14) Myers, A. B.; Trulson, M. 0.; Pardoeen, J. A.; Heeremans, C.; Lugtenburg, J.; Mathies, R. A. J . Chem. Pfiys. 1986, 84, 633. (15) Tannor, D. H.; Heller, E. J. J . Cfiem. Pfiys. 1982, 77, 2021. (16) Page, J. B.; Tonks, D. L. J . Cfiem. Phys. 1981, 75, 5694. (17) Ainscough, E. W.; Bingham, A. G.; Brodie, A. M.; Ellis, W. R.; Gray, H. B.; Loehr, T. M.; Plowman, J. E.; Norris, G. E.; Baker, E. N. Biochemistry 1987, 26, 7 1. ( 1 8) Bangcharonepaurpng, 0.;Champion, P. M.; Martinus, S. A,; Fligar, S. G. J . Cfiem. Pfiys. 1987, 87, 4273. (19) Chanand, C. K.; Page, J. B. J . Chem. Pfiys. 1983, 79, 5234. (20) Stallard, B. R.; Callis, P. R.; Champion, P. M.; Albrecht, A. C. J . Cfiem. Pfiys. 1984, 80, 70. (21) Champion, P. M.; Albrecht, A. C. Annu. Reu. Pfiys. Cfiem.1982, 33,
353. (22) Lu, H. M.; Page, J. B. J . Cfiem. Pfiys. 1988, 88, 3508. (23) Myers, A. B.; Mathies, R. A. In Biological Applications of Raman Spectroscopy; Spiro, T. G., Ed.; Wiley: New York, 1987.
0 1990 American Chemical Society
R R Study of the Blue Copper Protein Azurin 11. Experimental and Curve Resolution Methods Protein Preparations. Samples of Pseudomonas aeruginosa azurin were prepared by established procedure^.^^^ Final purification was by gel chromatography on a Sephadex G-25 column (pH 7.0,O.Ol M potassium phosphate buffer) until the ratio of A625/A280 was 0.52. Samples for R R were prepared by dialysis of the azurin into the desired buffer and subsequent concentration by ultrafiltration or lyophilization. The protein was diluted to a final concentration of ca. 2 mM (absorbance ca. 1 mm-' at A, 625 nm). The A625/A280 ratio remained constant throughout this procedure when care was taken to perform the dissolution step in the cold (4 "C). Samples were then frozen and stored at -20 "C until needed for R R measurements. Spectroscopic Measurements. R R spectra were obtained by using either a SPEX 1403 equipped with a thermoelectrically cooled RCA C31034A photomultiplier tube, a Princeton Applied Research Model 1 1 12 photon-counting system, and a Nicolet 1 180E Raman data system or a SPEX Ramalog EU equipped with a cooled RCA 31034A photomultiplier tube, an ORTEC 9300 series photon counter, and a Nicolet 1180E Raman data system. Laser excitation was provided by a Spectra-Physics 171-01 Kr+ laser (413.1, 568.2, 647.1, and 674.6 nm) or a Coherent Radiation 590 or Spectra-Physics 375A tunable dye laser (Rhodamine 590 or Rhodamine 610 dye, 560-650 nm) pumped by a Spectra-Physics 17 1-19 Ar+ laser. Spectra were typically obtained with spectral slit widths of 3-5 cm-' and digital resolution of 0.2-0.4 cm-I. Spectral scan rates were 1-2 cm-' s-' with no analog time constant employed. Typical signal averaging utilized 9 or 16 coadded scans. The durability of the sample could be assessed during acquisition of a spectrum of observing the quality of any given scan. In some cases, up to 100 scans were averaged together. The experiments reported below were carried out at temperatures between 10 and 30 K. The cryogenic apparatus consisted of an Air Products Displex cryostat with a Lakeshore Cryogenics silicon diode controller. Laser power was typically 10 mW at the cryostat window. Temperatures quoted refer to nominal cryotip temperatures. Effects of local heating of the sample by the laser irradiation are discussed elsewhereS6 The sample cuvettes were cylindrical, 5-mm diameter by I-mm path length, with windows fashioned from Suprasil flats. The cryotip was fitted with a copper cold finger which held the cuvette with the maximum area in contact with the copper and only one window exposed. Good thermal contact was maintained by Dow-Coming silicone heat-sink compound. The angle of incidence of the laser beam upon the cuvette window was approximately 60°, the polarization was sagittal, and the Raman scattering was collected in the plane of incidence at 90" to the incident beam. Visible and ultraviolet spectra were obtained by using a Cary 17DX spectrophotometer. Measurements of pH were made by using a Radiometer PHM-64 research pH meter. Spectra at one wavelength, 647.1 nm, have been reported in a previous publication. The remaining spectra are similar in quality and in fact differ only in subtle quantitative fashion. Systematic variation among the spectra can therefore be best revealed via the curve resolution analysis. Consequently, we present data in this paper in the form of integrated peak areas. The procedures for accomplishing the curve resolution are described below. R R Peak Resolution and Area Determination. A central experimental problem in this study was the reliable determination of the areas of overlapping R R peaks. The digital spectral data were resolved by using the Nicolet standard software package for spectral peak analysis, CAP 11. This program is capable of determining the relative peak areas within a single spectral region (fundamental or O/C), given assumptions concerning the functional form of the peak line shapes (Lorentzian, Gaussian, or a mixture of each). The fundamental-to-overtone intensity ratios are determined by cutting out and weighing the total integrated band profiles. Results of the fitting procedure are shown in Figure 1 (raw experimental data) and Figure 2 (comparison of experimental spectra with the fitted curves). The quality of the fits is
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 2161 FUNDAMENTALS
OVERTONES
7
___1
100
-
I
FUNDAMENTALS
I
I
OVERTONES
Figure 2. Comparison of theoretical simulations (middle curve) with expanded experimental spectrum (upper curve). The lowest curves are the resolved peaks prior to synthesis into the observed spectrum.
reasonable; however, quantitative differences in relative peak amplitudes can be obtained as a consequence of varying model assumptions in the procedure. A particularly difficult problem in the curve resolution is the pair of fundamental peaks M and N which could not be resolved reliably and had to have their areas considered together rather than separately. In general, therefore, we report relative areas scaled to the sum of peaks M and N . An analysis of the separate intensities of the two peaks is presented below; it should be regarded as provisional. 111. Theoretical Approach Computational Methods. The theoretical methods used in this paper are described in detail elsewhere.'*2 The matrix method (MM) is a time domain formalism for computing absorption and R R intensities under the assumption that the ground- and excited-state potential surfaces can be treated as harmonic. Aside from numerical convergence questions (which are easily tested), the method produces exact results at 0 K using a decoupling assumption. At finite temperature, the decoupling approximation is typically a very good approximation, while an exact approach is available to check final results. Since the simulations in this paper address data taken at low temperature, the theoretically computed intensities are uniformly reliable. An advantage of the matrix method as compared to other time domain approaches is that overtone and combination intensities are produced automatically in each simulation. A typical calculation without mode mixing (but including frequency shifts) and involving 12 vibrational modes required about 10 CPU seconds on a Cray X-MP supercomputer to produce a complete set of excitation profiles for all fundamentals, overtones, and combinations. From these timing results, it can be seen that the method does not need a computer as powerful as the Cray to be of use. The computer code is structured so that the problem can be factored into coupled blocks, with the block size determined by the number of modes coupled by mode mixing. As stated above,
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The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
the lack of resolution in the overtone region prevents a reliable quantitative exploration of mode mixing in the present paper. However, this capability is easily turned on and off in a single, automated code, making such explorations straightforward (see, e.g., ref 3). Strategies for Fitting Experimental Data. In analyzing the experimental results, our first step is to scale the integrated intensities of each observable Raman peak to that of the most intense fundamental. This yields a set of relative intensities at each wavelength. To compare the theoretical absolute intensity of the most intense fundamental with experimental values requires extracting absolute intensities from the latter, e.g., by comparison with a known internal standard. In this paper, this type of analysis will not be undertaken; such studies will, however, be pursued in future work, as they should provide a useful cross check for the approach used here. The relative intensity of each fundamental to the most intense one is principally determined by the ratio of the linear excited-state displacements of the corresponding vibrational modes. Thus, once the magnitude of one linear displacement is determined, the rest can be (roughly) scaled to this value, at least for small or moderate values of the displacement. However, without any additional constraints, a large number of sets of linear parameters can provide an adequate fit to the fundamental intensities, with the absorption spectrum width appropriately adjusted by altering the homogeneous or inhomogeneous broadening factors. In our numerical experiments, excitation profiles do not appear to allow one to choose between these alternate parameter sets if the absorption band is featureless (as it is in a large number of biologically important systems, including the one presently under study). This ambiguity can, however, readily be resolved by utilizing the O/C region in addition to the fundamentals. When the proper scale factor for the linear displacements is selected, all of the theoretical overtone and combination intensities take on values quite close to the experimental ones. As will be shown in the results section, failure to impose this constraint can lead to uncertainties as large as a factor of 2 in the magnitude of the linear coupling constants, despite the use of the absorption line width as a constraint. (All of the parameter sets in the results section accurately reproduce the absorption spectrum.) Furthermore, absolute intensity measurements are not guaranteed to resolve this ambiguity, because the ratio of homogeneous-to-inhomogeneous broadening can be adjusted (again, without substantially perturbing the absorption spectrum) to fit this piece of data for each of the linear coupling sets. In the present calculations, when the O/C region is employed, the greatest source of error is in fact uncertainty as to the proper experimental intensities, as opposed to the range of solution permitted by the theoretical fitting procedure. Once a reasonable set of linear displacements is determined (e.g., by fitting the relative intensities at a single wavelength), one can then attempt to determine quadratic parameters (mode mixing and frequency shifts). A surprising result of our studies is that (at least for the present system) relative excitation profiles of fundamentals are primarily sensitive to relative excited-state frequency shifts. That is, two modes with roughly equal quadratic displacements will display a flat relative excitation profile while a significant increase in the quadratic coupling of one mode as compared to the other will lead to a linear relative profile that is tilted at an angle, the magnitude of the angle depending upon the difference in frequency shift. An example of this behavior will be given in the results section. We should emphasize here that this observation is a tentative one and will have to be confirmed in the study of a large number of different models before it can be assumed to be generally applicable. If it is correct (or if some variant is correct), then a rather straightforward procedure for directly estimating excited-state frequency shifts from RR experiments without going through extensive simulation procedures could be developed. The approach discussed above allows one to obtain relative frequency shifts. However, one still needs to determine the absolute frequency shift of at least one mode. This can be accom-
Belhadj et al. plished by fitting the relative excitation profiles of the O/C region. In this paper, we choose to fit the integrated intensity of the O / C region as compared to the most intense fundamental, principally because the curve resolution in the O/C region is problematic due to the presence of overlapping bands. We do not believe that the accuracy of the values obtained is high, although the fit with quadratic coupling is definitely distinguishable from that utilizing linear coupling only. The quadratic parameters presented in the next section should therefore be taken as qualitative estimations. Mode mixing should manifest itself most unambiguously as disagreements between the theoretical and experimental relative intensities of overtone and combination bands of the modes thought to be involved. The imprecision of the curve resolution in the O/C region is here a very serious problem, and we have concluded that a quantitative investigation along these lines is not warranted by the present data set. There are systematic discrepancies of the above type in the fits obtained without mode mixing, which future experimental studies may allow us to investigate. The above provides an outline of the fitting procedure employed in this study; first determine a set of linear parameters from the fundamental and O/C intensities and then use excitation profiles to extract frequency shifts. The procedure must be iterated several times to provide the best overall fit to the entire data set. We do not present formal error estimates because much of the error (e.g., that coming from the experimental noise and inaccurate curve resolution) may be systematic in nature. However, the solutions are reasonably stable in that we have not found alternate parameter sets that differ greatly from the ones given below that lead to equally acceptable results. Quantitation of error estimates awaits (as do many possible improvements of our methodology) the generation of more precise experimental data sets. IV. Results and Discussion Representation of the Excited-State Potential Surface. Before proceeding, we briefly discuss the parameters used to describe the excited-state surface and their interpretation. In the M M formalism, the most convenient form of the excited-state Hamiltonian is in second quantized notation utilizing creation and annihilation operators, i.e.
Here bi and b> are the usual boson annihilation and creation operators, respectively, the wi are the ground-state vibrational frequencies, the gi are the shifts of the equilibrium positions of the normal modes in the excited state (linear coupling parameters), and the uij are frequency shifts (diagonal) and mode mixing parameters (off-diagonal). Each of the above parameters (w, g, and u ) is properly expressed in energy units, e.g., wavenumbers. In what follows the unit of energy is scaled to the value in wavenumbers of the highest frequency fundamental, 753 cm-I. The parameter sets reported below are expressed in these units. A conversion of the linear coupling results into physically transparent information (e&, equilibrium bond length changes) requires knowledge of the ground-state equilibrium geometry and a normal-coordinate analysis. In the absence of such information, one can compute dimensionless normal-coordinate (DNC) values A; this is done only for the best-fit results in Table V. (Note that the signs of the parameters, presented here as positive, are in fact not directly obtainable from the present RR intensity analysis.) Similarly, we calculate excited-state vibrational frequencies in wavenumbers for each Raman-active mode for the best fit. The formulas connecting the energy parameters of eq 1 with the physically relevant DNC and excited-state vibrational frequency we are we = [(UP)* + 2uwq1/* (2a) Fitting Procedure and Parameter Sets. In addition to our best-fit parameter set, we examine in detail five alternate parameter sets (chosen from a much larger subset that we have generated) in order to address several important qualitative issues.
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 2163
R R Study of the Blue Copper Protein Azurin
TABLE I: Comparison of Experimental and Calculated RR Intensities of Azurin at 627 nm for Various Parameter Sets
peak G H K
L M+N
0 P
Q R
W L+N 2M 2N N+O 20
freq, cm-'
exptl intensity
case 1
case 2
calcd intensities' case 3 case 4
case 5
case 6
265 286 348 372 400, 408 428 44 1 454 473 753 779 802 814 836 856
0.127 0.091 0.070 0.336
0.125 0.092 0.07 1 0.374
0.125 0.091 0.071 0.370 1.oo 0.331 0.101 0.053 0.052 0.158 0.156 0.143 0.240 0.145 0.056
0.122 0.090 0.071 0.351 1.oo 0.329 0.104 0.053 0.052 0.128 0.140 0.142 0.203 0.151 0.054
0.126 0.093 0.072 0.346 1.oo 0.334 0.103 0.052 0.051 0.010 0.046 0.023 0.093 0.050 0.010
0.125 0.091 0.07 1 0.37 1.oo 0.323 0.096 0.025 0.024 0.305 0.074 0.316 0.197 0.077 0.033
1
.oo
0.345 0.099 0.042 0.021 0.155 0.148 0.141 0.21 1 0.162 0.085
1
.oo
0.333 0.100 0.051 0.050 0.164 0.158 0.157 0.240 0.144 0.056
'Intensities are relative intensities scaled to the intensity of
M
+ N.
These are the following: ( I ) How unique is the fitting procedure if the O / C region is not utilized? (2) How well does a model that incorporates only linear coupling parameters perform? (3) What is the effect of assuming different percentages of homogeneous and inhomogeneous damping; Le., can we extract this ratio from our simulations? Two technical points in the fitting are worth discussing before proceeding to an examination of the results. First, the strongest Raman peak, at 408 cm-l (labeled N in Table I), overlaps considerably with a second peak at 400 cm-l (labeled M). The curve resolution of these two peaks is particularly difficult because of this substantial overlap. Consequently, in our analysis of the remaining peaks in the spectrum, we scale the intensities to the sum of the intensities of M + N, which is a much more stable quantity. A separate analysis of the relative excitation profile of M with respect to N is also performed; the results of this are clearly problematic (as will be apparent below) but provide some estimates of the partitioning of the Franck-Condon factors between these two modes and their relative quadratic coupling. Second, a one-to-one assignment of peaks obtained from the curve resolution in the O / C region to theoretical peaks is not possible, due to the large numbers of closely spaced overtones and combinations that can be generated from the set of fundamentals. We therefore group together several nearby theoretical peaks into a single number which is then compared with the experimental intensity. For example, the peak labeled 2N in Table I actually contains the combination band M N as well. Table VI contains a complete mapping of the theoretical peaks into a set of effective intensities, which are then labeled as in Table I. This procedure, of course, implies certain limitations upon the accuracy with which comparisons in the O/C region can be made. Table I compares the experimental intensities of the Raman peaks (relative to M + N ) with a 627-nm excitation wavelength (this is the absorption maximum). The six cases displayed in Table I represent six parameter sets given in Table 11. A short description of the significance of each case is presented in Table 111; extended discussion of these models will appear below. The first significant feature of Table I to note is that every parameter set listed provides an adequate fit in the fundamental region. (The small discrepancy associated with peak L is a consequence of fitting the excitation profile for this mode and will be discussed in detail below.) Of particular importance in this regard are parameter sets 4 and 5 , which represent fits employing small and large damping constants (and hence yield large and small linear coupling parameters, respectively). The parameters for these two cases differ from each other by a factor of 3, and the best-fit case (case 1) is positioned between them. We therefore conclude that utilization of only the fundamental region is grossly inadequate for the quantitative determination of excited-state structure from RR data, at least for the system examined here. Obviously, simulations need to be carried out for a wider class of molecules before the generality of this conclusion can be as-
+
0.128 0.094 0.073 0.341 1.oo 0.336 0.105 0.053 0.053 0.163 0.234 0.220 0.360 0.260 0.092
TABLE I 1 Parameter Values for Azurin Simulations at 627 nma
freq, cm-'
case 1
case 2
case 3
case 4
case 5
case 6
265 286 348 372 400 408 428 441 454 473 753 372 400 408 428
0.136 0.117 0.104 0.232 0.282 0.387 0.225 0.126 0.09 0.09 0.125 -0.115 -0.13 -0.05 -0.04
0.170 0.146 0.130 0.290 0.352 0.484 0.280 0.158 0.115 0.115 0.156 -0.115 -0.13 -0.05 -0.04
0.132 0.114 0.102 0.228 0.294 0.387 0.223 0.126 0.09 0.09 0.125 0.00 0.00 0.00 0.00
0.204 0.176 0.156 0.338 0.440 0.581 0.338 0.189 0.135 0.135 0.188 0.00 0.00 0.00 0.00
0.066 0.057 0.051 0.113 0.147 0.194 0.113 0.063 0.045 0.045 0.063 0.00 0.00 0.00 0.00
0.025 0.024 0.029 0.037 0.048 0.11 0.07 0.043 0.022 0.022 0.040 -0.115 -0.13 -0.05 -0.04
LZ GS
0.715 0.315
0.95 0.00
0.72 0.33
0.40 0.20
0.85 0.33
0.00 0.95
'Parameters in units of the highest vibrational frequency, 753 cm-I. TABLE 111: Qualitative Description of Cases 1-6
case 1 2 3 4 5 6
description best fit fit with Lorenztian damping only fit with linear coupling only fit to fundamentals only (small damping) fit to fundamentals only (large damping) fit with Gaussian damping only
sessed. In fact, it is quite possible that the existence of a vibronically structured absorption profile is sufficient to remove the greatest part of the ambiguity. We next ask whether a strictly linear coupling model is adequate to reproduce the full experimental data set. Cases 2 and 3 represent two such attempts, with differing amounts of Gaussian broadening. (This issue will be discussed below.) For 627 nm, the quality of the fits are roughly equivalent to that of the best-fit case. Therefore, we must examine excitation profiles to proceed further. Table IV and Figure 5 compare the experimental relative intensity of the integrated O/C region as a function of wavelength with that obtained from various theoretical models. Case 1 explicitly includes frequency shifts for modes L, M, N, and 0, the strongest of the fundamentals. There is significant improvement in the shape of the excitation profile for this case as compared to cases 2 and 3. (Case 4 and 5 are grossly in error, as discussed above; case 6 will be considered below.) However, we do not believe that the reliability of the precise value of the quadratic coupling constants in Table I1 is very high, both because of uncertainties in the experimental results and because we have not
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The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
TABLE I V Integrated Intensities for the Overtone Region for Cases 1-6’ exptl freq, nm intensity case 1 case 2 676.4 0.703 0.739 0.620 647.1 0.865 0.861 0.835 627 0.902 0.900 0.896 597 0.870 0.898 0.879 568 0.824 0.810 0.736 Olntensities are relative intensities scaled to the intensity of M
Belhadj et al.
calcd integrated intensities case 3 0.571 0.750 0.838 0.903 0.874
G H K L M
N 0 P
Q
R W
fr eq , cm-‘
linear
dimensionless
265 286 348 372 400 408 428 44 1 454 473 753
0.136 0.117 0.104 0.232 0.282 0.387 0.225 0.126 0.090 0.090 0. I25
0.550 0.435 0.320 1.215 1.480 1.244 0.650 0.302 0.212 0.202 0.177
quadratic
case 6 0.713 0.737 0.760 0.804 0.879
7 excited S T E freq
-0.1 15 -0.13 -0.05 -0.04
271 285 367 398
q
- - ?E E” t;
#
.................... 1
:: 0
560.00
580.00
600.00
620.00
IO. 00
650.00
640.00
WAVE LENGTH
Parameters other than “dimensionless” are in units of the highest vibrational frequency, 753 cm-I.
TABLE VI: Experimental and Theoretical Raman-Active Modes of Azurin calcd position, peak cm-‘ assignt W 153 W K+M 146 K+N 753 783 L + N L+N 776 K+O 79 1 K+P L + M 776 2M 798 2M 798 K+Q 806 L + O 813 2N 2N 821 K+R 821 L+P 806 M+N N + O 836 N+O 828 L+Q 828 M+O M + P 843 N + P 855 20 M + P 857 859 20
case 5 0.202 0.280 0.336 0.408 0.441
+ N.
TABLE V: Dimensionless Displacements and Excited-State Frequencies for Best Fit (Case 1) couuline. uarameters’ peak
case 4 1.080 1.290 1.360 1.380 1.300
Assignment of the exptl peak W
position, cm-’ 753
L + N
783
Figure 3. Excitation profile for peak 0.The data plotted are the ratio of the intensity of this peak to that of peaks M + N as a function of wavelength: (m), experimental points; (-), 3; (---),case 4; (---),case 5.
case 1 (best case);
(.e.),
case
z 0w I-
z
Y
2M
798
2N
813
N+O
836
WAVELENGTH
859
Figure 4. Excitation profile for peak L. The data plotted are the ratio of the intensity of this peak to that of peaks M N as a function of wavelength: (m), experimental points; (-), case 1 (best case); case 3; ( - - - ) , case 4; (---), case 5.
560.00
580.00
600.00
620.00
640.00
I. 00
660.00
+
(-e),
20
thoroughly investigated the uniqueness of the fit. More precise studies will be carried out with more accurate data sets in the future. Additional information concerning quadratic coupling can be obtained from the relative excitation profiles of the fundamentals. We first consider the excitation profile of peak M (scaled now to only peak N), shown in Figure 6 and compared with various model results. As stated above, the curve resolution of this peak is difficult to achieve because it overlaps substantially with peak N. It is therefore quite likely that the irregular shape of the experimental curves is an artifact of the fitting procedure. All of the experimental relative excitation profiles are in fact nearly straight lines, a consequence of the large damping parameters (experimentally manifested in the smooth, featureless shape of the absorption spectrum) and the small to moderate values of the linear displacements. Note, however, that the slope of the excitation profile is controlled by the relative quadratic coupling of the two peaks. The profile of case 1 represents an approximate
-n
c
__---
- - - - _ _-
-
.... ...
--
+
0 0
-
1
560.00
580.00
600.00
620.00
640.00
6 1. PO
660.00
WAVELENGTH
Figure 5. Integrated intensities for the overtone regtion as a function of wavelength: (m),experimental points; (-), case 1 (best case); case 2; (- - -), case 4; (---), case 5 . (e-),
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 2165
RR Study of the Blue Copper Protein Azurin
a
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Figure 6. Excitation profile for peak M. The data plotted are the ratio of the intensity of this peak to that of peak N as a function of wavelength:
(m), experimental points; (-), case 1 (best case);
4; (---),
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case 3; (---),case
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Figure 7. Excitation profile for peak M + N. The data plotted are the ratio of the absolute intensity of this peak scaled to that of peaks M + N at 627 nm: (m), experimental points; (-) case 1 (best case).
case 5 .
straight line through the experimental points. In view of the noise fluctuations, we did not attempt to quantitatively generate a “best” (e.g., in the least-squares sense) fit. Figures 3 and 4 display similar results for the relative excitation profiles of peaks 0 and L, scaled to the sum M N (which is dominated by N because of its larger intensity). The flat profile of 0 is reproduced simply by using the same (small) quadratic coupling value for 0 as for N . In the case of L, it is again clear that the fitting procedure has distorted the proper shape of the profile. If one believes the rise in relative intensity at 676 nm (this is in fact confirmed by a variety of differing curve-fitting approaches), then the sloping line of case 1 generated by an enhanced quadratic coupling value is appropriate. This particular parametrization must obviously be regarded as quite uncertain, pending the extraction of more accurate wavelength dependence. We next examine the effect of changing the amount of homogeneous versus inhomogeneous broadening included in the effective Hamiltonian. The best way to experimentally access this ratio is via absolute intensities, as indicated in ref 13 and 14. In the absence of this information (which is not trivial to obtain experimentally), we look at the excitation profile of the integrated O / C intensity under the assumption of different ratios. Gaussian broading leads to a less extreme falloff of the relative intensity in the wings as compared to the absorption maximum. This is demonstrated in cases 2 and 6, which correspond to 0% and 100% Gaussian broadening, respectively. Case 1, the best fit, utilizes primarily homogeneous damping but includes a small inhomogeneous component. As in the case of the quadratic parameters, we do not consider this number to be very reliable. However, it does constitute a prediction of the damping parameters which can now be checked via the more accurate absolute intensity approach. If the latter yields a very different answer, the damping parameters could then be fixed to these values and the simulations redone. A last check on the consistency of the fitting procedure can be obtained by taking the ratio of peak N to a reference peak (here, a 200-cm-I mode of ice) plotting the result as a function of wavelength and assuming that the intensity of the ice peak remains constant. Figure 7 displays such a plot, normalized to the ratio at 627 nm. To compare this with the simulation results, we plot the absolute intensity of peaks M N, also normalized to unity at 627 nm, using the parameter set of case 1. While the overall agreement of the two curves is not unreasonable, there is a significant discrepancy in the position of the maximum amplitude, which is at 627 nm in the simulated profile and at 647 nm in the experimental one. We have been unable to resolve this discrepancy despite numerous attempts at parameter variation; Le., it has not been possible to shift the theoretical maximum into coincidence with the experimental one and retain any sort of consistency with the other experimental data. We do not have an explanation for this at present; perhaps there are problems with the experimental measurements, or perhaps our
+
+
search of parameter space has been overly restrictive. It is interesting to note that a similar red shift in the theoretical, as opposed to the experimental, excitation profile has recently been obtained by Champion and co-workers in their study of resonance excitation profiles from cytochrome P45O.I8 These workers were also unable to come up with a satisfactory explanation for the discrepancy, despite the introduction of non-Condon terms and multiple electronic excited states. Substantive thought needs to be given to this problem by both theorists and experimentalists. Finally, we briefly discuss the question of whether Duschinsky rotation parameters could be obtained for the azurin system. The O / C intensities in Table I do display systematic discrepancies between the theoretical and experimental results, which have not been possible to resolve by varying excited-state force constants (and keeping the remaining fitting constraints in agreement). However, it is our judgment that the quality of data and curvefitting procedure in the O / C region is not quite good enough to warrant an extensive investigation. Improved experimental data, however, should allow this type of study.
V. Conclusion This paper represents an initial attempt to exploit all of the available information in the integrated intensities derivable from protein RR spectra. There are clearly still many questions concerning the reliability of both the curve resolution and theoretical fitting procedures used above. However, these questions have been addressed in a different manner than has been previously used for analogous systems. The progress that has been made suggests that quantitative modeling procedures utilizing the O/C region are a fruitful direction in which to pursue theoretical and experimental research. The synthesis of this approach with that involving absolute intensity should be particularly valuable, as the confidence level with regard to parameter sets should increase substantially if one can accurately fit both types of data. The necessity of such cross checking is especially strong when, as in the present case, the absorption spectrum is broad and featureless. A relevant question at this point is to ask what purposes are served by obtaining accurate numerical values for the excited-state potential surface parameters. Several possible uses of these parameters suggest themselves. First, isotope substitution at the chromophore site has been shown to experimentally affect RR intensities; the prediction of such intensity changes can be used as a test of the ground-state chromophore force field if the excited-state structure relative to the ground state is known. If electronic structure calculations can establish the signs of the linear coupling parameters (this is a much less demanding task than accurately computing bond length changes), this information can be obtained from the type of analysis presented here. Because the observed intensity changes are typically rather small, quantitative precision will be a significant issue in the use of these experiments to refine chromophore force fields.
J . Phys. Chem. 1990, 94, 2 166-2 17 1
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A second possible approach would be to study a series of homologous proteins and/or model compounds and to establish empirical correlations between excited-state parameters and other properties of physical interest, e.g., redox potential, confinement of the motion of the Cu atom by the protein, etc. This has already been done in a simple manner in ref 17, in which an "intensityweighted" frequency in the 400-cm-' region was correlated with redox potential for a series of blue copper proteins. Because the above analysis processes observed intensity changes into welldefined molecular parameters, it should facilitate the construction and interpretation of available correlations. Experiences with utilizing this approach for ground-state frequency shifts suggest that important effects can be quite subtle and that, again, accuracy in the modeling procedure will be of value. Ultimately, calculations of the type proposed here must be carried out in conjunction with other approaches-electronic
structure computations, normal-coordinate analysis, molecular dynamics simulation-in order to develop, test, and refine groundand excited-state theoretical models for chromophore force fields and chromophore-protein interactions. The latter will require explicit simulation of RR line widths and their temperature dependence, a calculation that is quite feasible using the MM. Such an integrated strategy will permit full exploitation of the information contained in R R experiments. Acknowledgment. This work was supported in part by grants to R.A.F. from the N I H and NSF and by a grant to W.H.W. from the N I H (DK36263). R.A.F. is a Camille and Henry Dreyfus Teacher-Scholar and the recipient of a Research Career Development Award from the NIH, Institute of General Medical Sciences. Registry No. Azurin, 11 144-17-5.
Electrical Conductivity Behavior of Poly(L-glutamic acid) in NaCl Electrolyte Solutions. Effect of Poiyion Conformation A. R. Bizzarri, C. Cametti,* Dipartimento di Fisica, Universitri di Roma "La Sapienza", Rome, Italy, and Gruppo Nazionale di Struttura della Materia, Rome, Italy
and F. Bordi Laboratorio di Fisica, Istituto Superiore di Sanitd, Rome, Italy (Received: April 28, 1989; In Final Form: September 18, 1989)
The electrical conductivity of aqueous solutions of poly(L-glutamic acid) of three different degrees of polymerization has been measured as a function of polymer content at different NaCI concentrations, from lo4 to 3 X mol/L. The equivalent conductance of the polymer has been estimated from the slope in the plots of conductivity against the polyion concentration. The results are compared to the conductivity deduced from a simple additive relationship whose main contribution derives from the ion distribution in a spherical polyelectrolyte cell, on the basis of the mean-field Poisson-Boltzmann equation. This theory provides a quantitative description of the conductivity behavior of these polymer solutions in a wide range of salt concentrations and polyion densities. As the electrostatic interactions of small ions in the neighborhood of the polyion become stronger and the polymer conformation deviates from the spherical random coil structure, the transition to counterion condensation occurs, providing support for the concept of an effective charge in linear polyions in solution, smaller than their titration charges. In this context, the conductivity of the polyion of lowest molecular weight is found to agree reasonably well with the predictions of the Manning theory.
Introduction Considerable progress has been made in understanding a wide variety of thermodynamic, transport, and conformational properties of natural and synthetic polyelectrolytes, including highly charged biopolymers, on the basis of the counterion condensation This theory, based in its first formulation on the two-phases model and derived as a consequence of the free energy minimization, has been a subject of theoretical and experimental According to this theory, for linear polymers, when the charge density parameter
exceeds a critical value &, a fraction 1 - 1/€1z1of charged groups of the polyion is neutralized by counterions to reduce the effective charge to a constant value. Here, /B is the Bjerrum length, at which two electronic charges e in a solvent of permittivity 6 interact with an energy kBT;z is the counterion valence; b is the charge *Address correspondence to this author at Universitl di Roma "La Sapienza".
0022-3654/90/2094-2166$02.50/0
spacing along the polyion contour. On the other hand, when 5 is lower then tC,the polyion charge equals its stoichiometric value and the entire population of counterions is distributed over the whole volume of the solution. The approach to thermodynamic and hydrodynamic properties based on the Poisson-Boltzmann theory largely supports counterion condensation theory, in particular with regard to transport and colligative properties.8-'0 In contrast, for highly flexible polyions, where the coiling of the polymer makes it possible to describe the transport properties on the basis of the two-state model, the counterion condensation does not occurs in the limit of infinite dilution, although the ion (1) (2) 191. (3) (4)
Manning, G. S. Q. Rev.Biophys. 1978, 11, 179. Anderson, C. F.; Record, M. T., Jr. Annu. Rea Phys. Chem. 1982, 33,
Manning, G. S . Biophys. Chem. 1911, 7, 95. Manning, G. S. J. Phys. Chem. 1981, 85, 1506. (5) Zimm, B. H.; Le Bret, M. J. Biomol. Strucl. Dyn. 1983, 1 , 461. (6) Manning, G. S. J. Phys. Chem. 1980, 84, 3331. (7) Woodbury, C. P., Jr.; Ramanathan, G. V . Macromolecules 1982, I S , 82. (8) Cametti, C.; Di Biasio, A. Ber. Bumen-Ges. Phys. Chem. 1986,90,621. (9) Le Bret, M., Zimm, B. H. - Biopolymers, 1984, 23, 287. (IO) Bordi, F.; Cametti, C.; Di Biasio, A. Ber. Bunsen-Ges. Phys. Chem. 1981, 91, 737.
0 1990 American Chemical Society
