J. Phys. Chem. 1983, 87,359-367
359
Sensitivity of V,’ Saturation Transfer Electron Paramagnetic Resonance Signals to Anisotropic Rotational Diffusion with [‘5N]Nltroxide Spin-Labels. Effects of Noncoincident Magnetic and Dlffuslon Tensor Principal Axes A. H. Beth,’+ K. Balasubramanlan,+ B. H. Robinson,$ L. R. Dalton,* S. D. Venkataramu,+ and J. H. Park’ Departments of Physiology and Chemistry, Vanderbilt University, Nashvllk Tennessee 37232; Department of Chemistry, University of Washington, Seattk, Washlngton 98195; and Department of Chemistry, State University of New York at Stony Brook, Stony Brook, Long Islend, New York 11794 (Received: July 21, 1982)
We have examined the sensitivity of the widely employed second harmonic out-of-phase absorption EPR signal ( V i ) recorded under conditions of partially saturating microwave and nonlinear Zeeman modulation fields to anisotropic Brownian rotational diffusion at X- (9.45 GHz) and K-band (22.0 GHz) microwave frequencies. [15N,2H]spin-labels have been utilized in order to minimize computation times and provide high resolution of major and minor element spectral structurings. Simulations of experimental isotropic model system V i spectra obtained from [15N,zH]maleimidespin-labeled glyceraldehyde 3-phosphate dehydrogenase (GAPDH) at X band are shown for correlation times of 2, 20, and 100 I.LS as well as in the rigid lattice limit. Optimization of the agreement between these experimental and simulated isotropicmodel system spectra provided reasonable magnetic parameters and relaxation times for calculation of spectra to be expected for anisotropic rotational diffusion of nonspherical molecules in isotropic medium. We have examined the line-shape behavior of the V i signal for prolate ellipsoids of variable axial dimensions with the spin-label principal magnetic axis aligned with the major ellipsoid axis. This sequence of spectra gives valuable insight into line-shape changes in separate regions of the spectrum which are determined by rotational motions about the D,, and D, molecular axes. We have also examined the line-shape effects of nonalignment of the magnetic and diffusion tensors arising from tilt of the spin-label from the diffusion axis of a long cylindrical molecule. This model is consistent with the rotational diffusion behavior to be expected for many intrinsic membrane spanning proteins which do not exhibit large amplitude rotation or oscillation about an axis perpendicular to the membrane normal. The calculations indicated the following: (1)The rotational diffusion contributions to the V i line shape can be quantitatively reproduced for isotropic Ehownian rotational diffusion of a protein over a wide range of correlation times. (2) The V i spectrum from [1!’N,2H]-labeledbiomolecules is sensitive to the anisotropy of the rotational diffusion as well as the geometric anangement of the spin-labelrelative to the ellipsoid of revolution. (3) Spectral sensitivity to minor element (x-y nitroxide axes) averaging with 15Nspin-labels and hence sensitivity for determining both D,, and D, can be enhanced by utilizing higher-frequency 22.0-GHz measurements. (4) Utilization of multiple observational frequencies greatly enhances rigorous definition of all elements of the diffusion tensor.
Introduction Since the introduction of the technique by Hyde and Dalton,’ saturation transfer electron paramagnetic resonance (ST-EPR) spectroscopy has been employed to probe the rotational dynamics of a wide range of spin-labeled biomolecules. Subsequent to the introduction of commercial spectrometers and the publication of an experimental method for quantitating slow molecular dynamics by Thomas et al.? there has been a rapid proliferation of applications of the technique. Several reviews have appeared3+ which provide an overview of the systems and dynamic ranges which have been characterized. In most applications, the spectral inteinsity ratios C’/C, L”/L,and H”/Hdefined by Thomas e t a1.2 for [14N]maleimide spin-labeled hemoglobin in glycerol/ water solutions have been used to describe the rotational diffusion properties of the systems under investigation. The limitations of applying this method of isotropic model system analysis to systems which are undergoing anisotropic rotational reorientation have been realized by numerous investigator~.~,’-~~ Analysis of data by direct comparison of calculated and experimental V i ST-EPR spectra has been difficult in the past due to the excessive computation times required when nonlinear modulation and microwave field amplitudes are employed. f
Vanderbilt University.
* University of Washington.
#State University of New York at Stony Brook.
0022-3654/83/2087-0359$0 1.5010
Recently, Robinson and Dalton reported the computation of first harmonic out-of-phase dispersion ( V i ) signals arising from anisotropic rotational diffusion of molecules for cases where the diffusion tensor was either coincident with or orthogonal to the magnetic tensor principal axis.’ It was later demonstrated that the w, perturbation scheme of Galloway and Dalton14could be utilized to compute V i signals from 14N spin-labeled biomolecules while main(1) Hyde, J. s.; Dalton, L. R. Chem. Phys. Lett. 1972, 16, 568-72. (2) Thomas, D. D.; Dalton, L. R.; Hyde, J. S. J. Chem. Phys. 1976,65, 3006-24. (3) Hyde, J. S. In “Methods in Enzymology”; Hirs, C. H. W., Timasheff, S. N., Eds.; Academic Press: New York, 1978; Vol. 49G, pp 480-51 1. (4) Hyde, J. S.; Dalton, L. R. In “Spin Labeling 11: Theory and Applications”;Berliner, L. J., Ed.; Academic Press: New York, 1979; pp 1-70. - . ..
(5) Marsh, D. In “Membrane Spectroscopy”; Grell, E., Ed.; SpringerVerlag: New York, 1981; pp 51-142. (6) Hyde, J. S.; Thomas, D. D. Annu. Reu. Phys. Chem. 1980, 31, 293-317. (7) Robinson, B. H.; Dalton, L. R. J . Chem. Phys. 1980, 72,1312-24. (8) Johnson, M. E.; Hyde, J. S. Biochemistry 1981,20, 2875-80. (9) Beth, A. H.; Venkataramu, S. D.; Balasubramanian, K.; Dalton, L. R.; Robinson, B. H.; Pearson, D. E.; Park, C. R.; Park, J. H. Proc. Natl. Acad. Sci. U.S.A. 1981, 78, 967-71. (10) Beth, A. H.; Balasubramanian, K.; Wilder, R. T.; Venkataramu, S. D.; Robinson, B. H.; Dalton, L. R.; Pearson, D. E.; Park, J. H. (1981) Proc. Natl. Acad. Sci. U.S.A. 1981, 78, 4955-9. (11) Gaffney, B. J. J. Phys. Chem. 1979,83, 3345-9. (12) Delmelle, M.; Butler, K. W.; Smith, I. C. P. Biochemistry 1980, 19, 698-704. (13) Robinson, B. H.; Dalton, L. R. Chem. Phys. 1979, 36, 207-37. (14) Galloway, N. B.; Dalton, L. R. Chem. Phys. 1979, 41, 61-6.
0 1983 American Chemical Soclety
360
The Journal of Physical Chemistry, Vol. 87, No. 2, 1983
Beth et ai.
TABLE I: Electron-Zeeman (g) and Nitrogen-Hyperfine ( A ) Tensor Values for [ lSN,ZH]MSL-LabeledGAPDH in Different Environments 53% glycerol ( w t i w t ) 78% glycerol ( w t i w t ) 89% glycerol ( w t i w t ) AS-precipitatedb bound t o band 3'
gxx
gY Y
gzza
2.0087 2.0091 2.0089 2.0086 2.0088
2.0056 2.0061 2.0060 2.0058 2.0060
2.0022 2.0022 2.0022 2.0022 2.0022
4 x 3
G
10.85 10.62 10.85 10.50 11.30
A,,, G 10.35 10.38 10.60 10.40 11.00
A,,, G 50.45 50.15 50.30 51.25 49.75
a A value o f 2.0022 for g, was arbitrarily chosen in each calculation and the other tensor elements calculated relative t o it. The microwave frequency and magnetic field strength were not calibrated t o the degree o f accuracy necessary t o report The abbreviation AS is for ammonium sulfate. an absolute number for g z z , Details of binding o f GAPDH t o the c y t o plasmic aspect of band 3 protein in the human erythrocyte membrane can be found in ref 10.
'
taining acceptable computation times.I5 By utilizing the computational simplification afforded by [ 15N]nitroxide spin-labels, we have been able to extend these calculations to full inversion of the supermatrix problem including the effects of nonalignment of the magnetic and diffusion tensor s y s t e m ~ . ~Using J ~ this computational approach we have characterized the rotational motions of both soluble and membrane-bound forms of the enzyme glyceraldehyde 3-phosphate dehydrogenase (GAPDH) by direct simulation of experimental V,' spectra.l0 In this report we describe trends in spectral parameters obtained from calculated V i spectra at X- and K-band microwave frequencies for systems undergoing axial anisotropic Brownian diffusion. Sensitivity to motional averaging about the D,, and D, rotational axes is demonstrated and the effects of noncoincident diffusion and magnetic tensor axes are examined. A rigorous comparison of experimental and calculated V i signals demonstrates the potential of a computational approach for defining elements of the diffusion tensor for spin-labeled biomolecules.
Methods Computer Simulations. The computational approach reported by Robinson and Dalton7J3J5was used to calculate V i line shapes. The electron-Zeeman (g) and nitrogen-hyperfine (A) tensor axes were assumed coincident. For noncoincident diffusion and magnetic tensors, the angle 8, was generated by a rotation about D, and A,, which were arbitrarily chosen coincident (see hgure 1). Similarly, the angle ,e, was generated by a rotation about D,, which was chosen coincident with A,,. A comprehensive discussion of the theory and definition of correlation times was given in previous work.' Pseudosecular and saturation terms of the spin Hamiltonian are explicitly included as is the interaction of the electron spins with the applied Zeeman modulation field. All line shapes were postconvoluted with a Gaussian function to simulate the inhomogeneous broadening of the unresolved deuterium superhyperfine coupling. Calculations were done on either a DEC-1099 or a PDP-VAX 11/780 computer. The tensor values used in all calculations were obtained by simulation of Vl signals from [ 15N,2H]MSL-labeled(MSL = 4-maleimido-2,2,6,6tetramethylpiperidinyloxy)GAPDH in this and previous workgJOand are summarized in Table I. Relaxation times were estimated by obtaining the best fit of the isotropic model system spectra from soluble GAPDH in glycerol/ water solutions and were scaled to simulate the effects of overmodulation as discussed by Robinson.16 Experimental Model System Spectra. Reference spectra for isotropic Brownian rotational diffusion were obtained from [15N,2H]MSL-labeledGAPDH in glycerol/buffer solutions of 53%, 77%, and 89% (wt/wt) which (15) Robinson, B. H.;Dalton, L. R. Chem. Phys. 1981, 54, 263-9. (16) Robinson, B. H.J. Chem. Phys., in press.
\\
' k
,'
3 DY Y
Figure 1. Relationship between magnetic and diffusion tensors for a nitroxide spin-labeled molecule. The magnetic tensor axes are labeled A,, A,, and A, while the elements of the diffusion tensor are D,, D,, and 0,. The two coordinate systems are related by a single angle 8, which is generated either by a rotation about A, and D, through 8, or about A, and D, through 6,. The A and g magnetic tensor systems are assumed cdncident as are the d W i and inertial tensor systems. In all calculations Involving anisotropic models we have confined ourselves to an axially symmetric diffusion tensor with D, = D, = D , and D, = Dll. The elements of the diffusion tensor are related to the correlation times through the relationship D = 1/(67,) and D,, = 11(6~,,).For isotopic diffusion models, D, = D, = DLI and the diffusion coefficient is related to the correlation time through the relationship D = 1467.J.
,
gave rotational correlation times of 2,20, and 100 ps, respectively. The powder" spectrum was obtained from ammonium sulfate precipitated GAPDH. The methods for preparing electrophoretically pure GAPDH and its spin-labeling with the [15N,2H]maleimidespin-label were the same as in previous r e p o r t ~ . ~ * ' ~Correlation **~ times were calculated from the Debye equation using a hydrated (17) The term Ypowder*is used to indicate that this is a hydrated polycrystalline sample in which overall rotational motion of GAPDH is prohibited. Line positions in linear EPR have reached their no-motion limit. Saturation transfer line shapes, however, are not at the no-motion limit for this sample due presumably to local motional processes. Calculated V i line shapes from eigenfunction expansion' and transition rate2 formalisms routinely yield H"/Hvalues of 2.0 or slightly larger as the correlation time for major-minor element averaging becomes longer than 10" s with 16N spin-labels. Enhancement of this parameter has been observed experimentally for a variety of systems (ref 18 and 19 and unpublished results) recorded at temperatures below 0 OC. (18) Johnson, M. E. Biochemistry 1981,20, 3319-28. (19) Johnson, M. E. Biochemistry 1978,17, 1223-8. (20) Gaffney, B. J.; Elbrecht, C. H.; Scibilla, J. P. A. J.Magn. Reson. 1981,44,436-46. (21) Beth, A. H.;Wilder, R.; Wilkerson, L. S.; Perkins, R. C.; Meriwether, B. P.; Dalton, L. R.; Park, C. R.; Park, J. H. J. Chem. Phys. 1979, 71,2074-82.
The Journal of Physical Chemistry, Vol. 87,No. 2, 1983 361
Sensitivity of V,’ ST-EPR Signals
radius of 41 A for the protein.21 Glycerol/buffer solutions were prepared on a wt/wt basis under a nitrogen atmosphere to avoid broadening effects due to molecular oxygen. The out-of-phase position for recording V i signals was estimated by the self-null method2 using a microwave power setting of 0.5 mW in the Varian E-238 cavity. A 50-lrHz field modulation of 5.0-G amplitude (peak-to-peak) and a microwave power setting which gave an HleHof 0.2 G in the rotating frame were used throughout. Experimental spectra were recorded with a Varian E-109 Century series spectrometer equipped with an E-272B f/f lock accessory and an E-257 variable-temperature accessory. Sample temperature was maintained at 2.0 f 0.5 “C by passing precooled air into the cavity through the radiation slots in the front. No sample Dewar was used to contain the WG-813 (Scanlon) flat cell. The sample was placed in the cavity in the position which gave the highest loaded cavity Q in each experiment. An on-line PDP 11/03 microcomputer was employed to drive the spectrometer and record signals digitally. Determination of H, and Hleff.The modulation sideband splitting of a 0.9 mM solution of peroxylaminedisulfonate (PADS) in nitrogen-equilibrated 10% K2C0, was used to calibrate the modulation field amplitude at the sample as described previously.21 Calibration of HleHwas accomplished by placing a 0.2-mm i.d. quartz capillary (Scanlon) filled with the same PADS solution used to calibrate H, inside the WG-813 flat cell which itself was filled with each of the glycerol/water solutions used to record the model system spectra of [15N,2H]MSL-labeled GAPDH. The power-induced line broadening of the mI = 0 resonance line was then recorded and plotted as A: vs. microwave power setting as shown in Figure 2. From this plot, Hleffwas determined by using the relationship =
b2+ 4T,Hleff2/(3TJ
(1) where Ae is the experimental line width as a function of power, Tland T, are the normal spin-lattice and spin-pin relaxation times, & is the intrinsic unbroadened line width, and Hleffis the “effective” microwave field amplitude in the rotating frame. Hleffis further related to Po through the relationship A:
Hleff = (KPo)1’2 where Po is the microwave power setting in watts.
(2)
Results The V i line shape has been shown to be dependent upon the amplitudes of the applied microwave and modulation fields at the sample.2 We have, therefore, determined the effective values of these parameters over the active dimensions of our model system GAPDH samples. Calibration of H, is straightforward and its amplitude does not vary with the composition of the glycerol/water samples used to record the model system spectra utilized in this work. The effective microwave field at the sample is strongly dependent on the dielectric properties of the sample and the dimensions of the sample holder. We have elected to measure the microwave observer field a t the sample by recording the power-induced broadening of a line sample of nitrogen-equilibrated PADS inserted into the flat cell with the remainder of the cell filled with one of the glycerol/water solutions. The curves in Figure 2 indicated that the loaded cavity Q when using a flat cell changed dramatically over the range of sample compositions studied. Using these curves, we have adjusted the microwave power level so that the isotropic model system spectra shown in Figure 3 were recorded at a constant
A,‘ (Gauss) ,k=O 93
/ 0.121
/
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/-
dE
0.10.
0.08
0.02
t
t ~.(Watts)
0 00
000
0 02
0 04
006
008
0 IO
0 12
Figure 2. Variation of H,, over the active dimensions of the WG813 flat cell. Along the ordinate we have plotted the square of the experlmentally measured line wldth of the m = 0 line from a line sample of PADS contained in a 0.2-mm i.d. quartz capillary insetted into the center of the flat cell against the microwave power setting in watts (abscissa). The data presented were obtained with the remainder of the flat cell filled with (0)5 mM phosphate buffer at pH 8.0, (B)53% 77% glyceroM mM phosphate glyceroV5 mM phosphate buffer, (0) buffer, and (A)89% glyceroV5 mM phosphate buffer. Details of the sample preparationare given in the Methods section. The solid lines were obtained by a llnear least-squares fit of the data. The cavity constants ( K ) for the various samples were calculated from the slope of the lines according to eq 1 and 2. In applying eq 1, we have assumed that T , , = T , for the PADS radical.
,
microwave observer field value of 0.2 G. This corresponded to power settings of 100,72, 52, and 41 mW for the ammonium sulfate precipitated 53%, 77%, and 89% glycerol (wt/wt) samples, respectively. The superimposed dashed lines in Figure 3 are the computer-simulated line shapes which gave excellent agreement between experiment and theory. The regions of the spectra dominated by both major-minor (2-x, z-y) and pure minor (x-y) element averaging processes for the &1/2 nuclear spin configurations were reproduced as the correlation time was varied experimentally from 2 ps to the rigid lattice limit. The approximate locations of the spectral turning points for the x , y,and z crystal orientations of the *1/2 15N nuclear states are shown along the lower edge of the bottom display. Detailed discussions of the V i signals behavior in regions near and between spectral turning points have been provided in previous work by members of this gr0up2JJ0J3and others.e~8~20 We note that in regions where dHr,/dQ is large (Le., in angular regions intermediate between magnetic principal axes) spectral intensities tend to rise monotonically relative to the turning points as the correlation time for molecular reo;ientation becomes longer than -lo4 s. In this slow to very slow tumbling region, the positions and intensities af spectral turning points are not highly dependent on correlation time. It will be helpful for subsequent discussion to define regions of the V i spectrum from 16Nspin-labelswhich are sensitive to the rate at which rotational motions about different spin-label axes are modulating the resonance condition. Spectral amplitudes in the regions L, L ”, H, and H“have been used previously for 14N-and 15N-labeledbiomolecules2,9v20and therefore will be maintained (Figure 4). Physically, the parameters L I’ and H”vary directly with
Beth et at.
362 The Journal of Physical Chemistry, Vol. 87, No. 2, 1983 -7,
v2
2 YLeC
200 Ysec
20 rrec 1
1,
10 G
1
2, 2 usec
Flgure 4. Calculated X-band V,’ line shapes for axial ellipsoids of variable dimensions. The correlation times about the 0, and 0, axes ( T ~ were ) increased from 2 to 200 ps along each row while the Correlation time about 0, (711) was Increased from 2 to 200 ps within each column. The magnetic and diffusion tensors are coincident (8, = ,8 = 0’). Increasing 711 in a given column leads to slower x-y nitroxide axis interconversion. Increasing 7L in each row leads to slower z-x and z - y interconversion. The field positions where the spectral parameters L , L “ , I‘, I I,, I”, H”, and Hare measured are indicated In the upper left spectrum. Line shapes were calculated by using the A and g tensor values from membrane-bound GAPDH given in Table I. Additional parameters included h , = 0.2 G, T , = 25 ps, T , = 40 ns, and a Gaussian postbroadening of 0.9 G.
Flgure 3. Experimental and calculated isotropic motion V,‘ model spectra. The solid lines are the experimental tracings obtained from [ i6N,2H]MSL-labeledGAPDH in glyceroil5 mM phosphate buffer soiutions of 53%, 78%, and 89% glycerol by weight giving correlation times (7c)of 2, 20, and 100 ps for the upper three displays. The lower spectrum was obtained from an ammonium sulfate preclpltated sample of [ ’%,2H]MSL-labeled GAPDH and therefore yields an infinite rotatbnal correlation time for complete rotation of the molecuie.” The superimposed dashed lines are the computer-simulated V,’ line shapes which were calculated by using the best-flt A and g tensor values from simulation of the corresponding linear EPR signals shown in Table I and the Indicatedcorrelation tlmes. Additional parameters included the following: h i = 0.2 G; T i = 25 ps; T , = 40 ns; and a Gaussian postbroadenlngof 0.5 G in the upper and lower and 0.9 G In the mlddle two spectra, respecthreiy. The lower spectrum was fled by using h , = 0.2 G, T i = 20 ps, T 2 = 60 ns, and a correlation time of 400 ps as discussed in ref 17.
the rate at which the z nitroxide axis is being averaged by motion into the x and/or y nitroxide axes. The amplitudes at L and H are largely independent of the motional averaging for correlation times longer than -lo* s. It should be emphasized that the spectral amplitudes measured at L”and H”are composite functions of z-x and z-y motional processes, and, for anisotropic diffusion, these may or may not be characterized by the same correlation times.
The parameters C and C’ defined by Thomas et al.,, which yield information on the rate of x-y and z-x interconversion with ‘*N-labeledbiomolecules, have no direct counterparts with 15N labels. There are, however, two areas of a I5N spectrum which exhibit sensitivity to the x-y motional rate. These are the angular regions intermediate between the x and y turning points of the *1/2 nuclear manifolds. These positions are labeled as I’and I”in the upper left spectrum of Figure 4. The spectral intensities at t h e y and x turning points of the -112 and +1/2 nuclear states, respectively, are labeled as Il and I,. In Figure 4 we have shown a 3 X 3 array of calculated V i line shapes at X band for isotropic and anisotropic motional models. 711 and 7L were varied by 2 orders of magnitude from 2 to 200 ps along the columns and rows of the array, respectively. The angle 8 between the nitroxide z principal axis and the axis of rotation defined by Dll (see Figure 1) is equal to zero in each display. This places the isotropic motion spectra at 2, 20, and 200 ks along the diagonal. Some interesting trends in the behavior of L”, I f ,I”,and H” as a function of the diffusional model are readily apparent. As 711is increased in a given column while 71 is held constant, spectral intensities in the I’ and I” regions build relative to the amplitudes measured at IIand 12,indicative of the slower x-y interconversion. The L”and H”regions are not modulated by this motional process and therefore remain essentially unchanged. This trend is shown graphically in Figure 5 (upper) where we have plotted the normalized parametric data from the three spectra in the central column of Figure 4 plus additional data calculated at parallel correlation times (711) of 9, 70, 700, and m ps. An examination of the same parameters from the central row of Figure 4 reveals a complementary trend. As T~ is increased from 2 to 200 ps while T , , is held constant at 20 NS, the L” and H” regions are enhanced relative to the spectral amplitudes measured at L and H, while the I’and 1”regions are less affected (Figure 5, middle). It is ap-
Sensitivity of V,' ST-EPR Signals
The Journal of Physlcal Chemistry, Vol. 87,No. 2, 1983 363
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Figure 5. Plots of normalized spectral ratio parameters vs. correlation times. Three motional models are presented. In each display the ( L " / L ( ~ ) ) / ( L " / L ( T = ~ )(,0 )( I ' / I , ( T ) / parameters are pbtted as (0) ( I ' l l ,(T=Lo)), (A)(I"/I&))/(I"/I AT= a), ( 0 )(H"/H(T)/(H"/H(7=m)). The Infinity parameters In each display were obtained from the lndependent variable (correlation time shown along the abscissa of each pbt) equal to 1 s. In the upper panel we have shown the parametric data for Zaxial diffusbn obtained from the three spectra In the center column of Figure 4 plus additional points for TI^ equal 9, 70, and 700 /IS and 1 s at a constant T~ of 20 ps. In the center we have shown the data from the central row of Figure 4 plus addltknal data calculated at r1 equal to 9, 70, and 700 ps and 1 s while holding 711 constant at 20 /IS. In panel c we have shown the data for the isotropic spectra along the diagonal of Flgure 4 plus additional data calculated for T~ equal 9, 70, and 700 ps and 1 s.
parent, however, that the spectral amplitudes measured at I'and I" are determined in part by the perpendicular averaging rate. If we construct plots of dHm/dQ vs. H,,,, we would find that there is appreciable motional modulation of the resonance condition in the I'region from z-y motion and in the I" region from z-x motion. This is
further evident by examining Figure 5 (lower) where we have shown the behavior of these normalized spectral ratios over a wide range of isotropic correlation times. For isotropic motion, the normalized parameters 1'/11and I'!/12 vary over a wider range of values than they do for slow x-y motion in the axial curves of Figure 5 (middle). Thus, just as H" and L" are composite functions of z-x and 2-y motional rates, I' is a composite of x-y and z-y while I" is a composite of x-y and z-x. The line shapes in Figure 4 were calculated by using tensor values obtained from erythrocyte membrane-bound GAPDHlO and therefore the isotropic spectra along the diagonal are not identical with the experimental model spectra of Figure 3. The choice of tensor values does not significantly affect these observations but rather only tends to shift curves along the independent correlation time axis. In applications where the spin-label is localized in a nonpolar environment such as encountered in lipid domains, there may be a coalescence of Il and I2into a single feature due to the smaller nitrogen-hyperfine anisotropy. Figure 6 shows the V i line shapes for various angular tilts of the nitroxide z principal axis from the major axis of a prolate ellipsoid characterized by correlation times of 2 ps ( T , , ) and 2 X s ( T J about the major and minor axes, respectively. As defined in Figure 1,, ,e or Ox, is the angle between the nitroxide z principal axis and the major axis of the ellipsoid produced by a rotation about Dy? or Ox,,respectively. When 0 is zero, this motional model gwes rise to fast x-y interconversion and the I' and I" regions are suppressed relative to a slow isotropic model (Figure 4, lower right). Conversely, z-x and z-y are very slow and therefore the L"and H" regions are enhanced. As Oyy. is increased from zero to 90" about A (Figure 6, x-axial model), the spectral shape changes d?amatically. In this orientation, z-y averaging is fast while z-x and x-y are very slow. This results in the L"and H"regions being a composite of fast and slow motional processes and, BS discussed previously,15the spectral amplitudes in these regions are intermediate between both being fast and both being slow (Figure 4,upper left and lower right). The I'and I" regions of the spectrum are asymmetric with respect to their appearance for an isotropic diffusion model due to the rapid z-y and slow z-x contributions being opposite for the f 1 / 2 manifolds in the regions where I' and I" are measured. When the line shapes for x-axial and y-axial motion are compared (Figure 6, bottom two spectra), we see that the asymmetry is reversed relative to an isotropic model (Figure 4,middle). For angles between 0" and 90" the line shapes and, hence, ratio parameters are intermediate between those for the aligned (0 = 0") and orthogonal (0 = 90") cases. Comparison of the 56" spectrum from Figure 6 with the isotropic spectra along the diagonal of Figure 4 indicates that at X-band microwave frequency this motional model and spin-label geometry gives rise to an isotropic appearing spectrum. An inspection of the minor element splittings in Figure 7 for 15N labels at X band indicates that x-y interconversion leads to spectral diffusion over a range of approximately 5 G for both the f 1 / 2 nuclear configurations. This small minor element anisotropy gives a limited sensitivity to motions which modulate these magnetic interactions. Sensitivity to a wider range of x-y motional frequencies can be realized by increasing the minor element anisotropy by higher microwave frequency operation. Nitroxide radicals typically show nearly axial nitrogen hyperfine ( A ) splittings while the field-dependent electron-Zeeman (g) interaction is highly anisotropic. We can take advantage of this field-dependent splitting to position
364
The Journal of Physical Chemistry, Vol. 87, No. 2, 1983
Beth et ai.
n
I
Flgure 6. Effects of nonalignment of magnetic and diffusion tensors at X band. This sequence of spectra was calculated for a motional model characterized by a correlation time ( q ) of 2 ps about the major axis and 2 X lo-* s ( T ~about ) the two minor axes of an ellipsold of revolution. The angle 0, was 0’ (Laxial), 30°, 56’, and 90’ (x axial) in the upper four spectra. The bottom spectrum was calculated wYh Om = 90’ o/ axial) for comparison with the 0, = 90’ immediately above. All spectra were calculated by using the tensor values and machine parameters listed in Figure 4 and each was postconvoluted with a Gausslan broadening of 0.9 G.
spectral turning points relative to one another in such a way as to increase expression of sensitivity to specific motional processes. This is illustrated in Figure 7 for calculated first harmonic in-phase signals (VI) at X- and K-band microwave frequencies. At 22 GHz the spectral turning points for the -112 spin state occur with the z turning point intermediate between x and y which are now separated by 12 G. This provides a highly resolved feature in the spectral display which is analogous in appearance to the mI = 0 component of a 14N spectrum (Figure 7 ) . Sensitivity to pure minor element x-y averaging should be improved in the -112 manifold of 15N at 22 GHz relative to 14N at 9.5 GHz, however, because of the increased separation of the minor element
‘ f z !‘ Y
f
Flgure 7. Turning points for the x, y and z niboxide crystal orientations. These calculated V , line shapes show the indhriual nuclear manifolds for a [15N]nitroxidein the no-motion limit both at X-band (9.45 GHz, upper) and K-band (22.0GHz, middle) microwave frequencies. Simulation parameters included the A and g tensor values from Flgure 4; T , = 6 ps; T , = 2 X lO-’s; and a Gausslan broadening of 0.9 G. The lower spectrum was calculated for a typical [“N]nitroxide at X band. Simulation parameters were as follows: ,A = 7.9 G;A, = 7.7 0;A, = 34.8 0; gp = 2.0088;g, = 2.0060;gu = 2.0022;T , = 6 ps; T , = 2 X 10- s; and a Gaussian broadening of 0.9 G. The field positions of the turning points for the -1/2 and +1/2 nuclear configurations of I5Nand for the +1, 0, and -1 nuclear configurations of I4Nare shown along the bottom edge of the corresponding display.
turning points. As shown in Figure 7 , the order of the turning points in the mI = 0 manifold from 14Nspin-labels is x , y, and z, respectively, as the field increases with a total
Sensitivity of V,’ ST-EPR Slgnals
The Journal of Physical Chemistry, Vol. 87, No. 2, 1983 “2
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0 01 10
1’: A
Flgure 8. Calculated K-band V,‘ line shapes. This sequence of spectra demonstrates the sensklvlty of V,‘ line shapes at K band (22.0 W r )for monitorlng x-y motional averaging. The spectra were calculated for a constant T~ of 20 ps and T l values of 2, 20 (isotroplc), 200 and in the rigid lattice limit. he fieb values where the spectral parameters I, 1’, H”, and H were measured are shown along the top edge of the upper spectrum. The magnetic and dlffuslon tensors are cdnckient (0 = 0’). Tensor values and machine parameters were the same as In Flgure 4 and each spectrum was postconvoluted with a Gaussian broadening of 0.9 G.
x-y anisotropy of approximately 6 G.
We have examined the potential utility of V i signals recorded at K-band (22.0 GHz) microwave frequency for enhancing sensitivity to anisotropic motions which modulate x-y nitroxide axis interconversion. In Figure 8, we show a series of spectra calculated for a constant majorminor element correlation time ( T J of 20 ps while rIlwas varied from 2 ps to the rigid lattice €imit. The region of the spectrum labeled I’ (Figure 8, upper) was found to vary directly with the rate of x-y interconversion. This parameter is measured at the z turning point of the -1/2 nuclear manifold which is intermediate between x and y. The regions of the K-band spectrum where HI’ and H are measured are not modulated by x-y motion (Figure 7) and therefore remain unchanged as rI1 is varied. This is shown graphically in Figure 9, where we have shown the normalized parametric data from the four spectra in Figure 8 plus additional points from spectra calculated at T ~of, 5 and 70 ps.
Discussion A common problem which has confronted experimentalists using saturation transfer techniques has been how to relate the spectral ratio parameters defined and mea-
10-5
10
,+
,
10
3
Llsecr
m
Figure 0. Plots of normalized spectral ratio parameters vs. T for K-band V,’ spectra. Only the z-axlal diffusion model is presented. (I’/I(Tl,))/(I’/I(T,l=~)) and ( 0 )( H ” / H ( T ~ ~ ) ) / Data are plotted as (0) ( H ” / H ( T ~ ~ = ~ )The ) . infinity ratios were obtained from the lower spectrum of Figure 8 which was Calculated with ril equal to 1 s. Additional points were obtained from calculations with T , equal ~ 5 and 70 ps.
sured by Thomas et aL2 for an isotropically diffusing protein to systems characterized by anisotropic motions. The use of anisotropic model systems to analyze experimental data by simple comparison of ratio parameters has been hampered by the lack of well-defined experimental systems which exhibit diffusional and orientational properties consistent with the problem under investigation. Recent ST-EPR studies by Gaffneyl’ on 4,4’-dimethylspiro[5a-cholestane-3,2’-oxazolidin]-3’-yloxy (CSL)included in thiourea adducts and by Delmelle et al.12 on the same label inserted into model oriented and dispersed lipid bilayers have provided insight into the behavior of the V i signal of well-defined experimental systems undergoing predominately y-axial jump motion (spin-label reference frame) in an orienting potential. We have now used a computational approach to model the motional contributions to the V2’line shape arising from isotropic Brownian rotational diffusion of a spin-labeled protein and then extended these results to include the effects of anisotropic Brownian motion of an axial ellipsoid of revolution for cases where the spin-label principal axis is aligned, orthogonal, or at intermediate angles with respect to the major axis of the ellipsoid. The results presented demonstrate the feasibility of a computational approach for determining the rotational diffusion characteristics of an arbitrary system provided that a unique static relationship between the spin and diffusion tensors exists and can be defined. We have utilized [16N,2H]spin-labels in this work to minimize computation time requirements and provide high resolution of spectral features as described previou~ly.~J~ It is instructive to correlate the motional sensitivity of the V i response from these labels with results obtained from the more widely used 14Nanalogues. The regions L,L”, H, and H”are analogous for the two nitrogen nuclei except for the total magnetic anisotropy of the manifolds. As noted by several investigators, these regions yield information on the rate at which molecular reorientation is modulating the resonance condition by interconversion of the z-x and z-y nitroxide axes. These two processes need not be characterized by the same rate for anisotropically diffusing systems and hence the ratios L ”/Land H”/H are composite functions of two correlation times. This is demonstrated experimentally by the axial diffusion curves from CSL in thiourea adducts by Gaffney” and inserted into model membranes by Delmelle et al.12 Plots of L”/L
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Beth et al.
The Journal of Physical Chemistry, Vol. 87, No. 2, 1983
or H”/H vs. temperature (or correlation time) for the y-axial models in these studies produced curves which minimize between the respective values observed for an isotropic model at the same correlation time and the nomotion limit. Plots of L”/Land H”/H vs. correlation time for isotropic diffusion show minima of near zero as the -10% s range for both correlation time increases in the I4N and 15Nspin-labels.2J0~20~21 A comparison of the lower two spectra of Figure 6 with the isotropic fast and slow spectra of Figure 4 (upper left and lower right) demonstrates the effect of one fast and one slow rate about the x and y nitroxide magnetic axes. A more complete set of correlation times for this motional model has been presented previou~ly.’~ It is evident from the spectra in a given column of Figure 4 and from the parametric data in Figure 5 (upper) that the x-y averaging rate has little effect on the L” and H” regions of the V i spectrum. Examination of the spectral turning points for the lower spectrum in Figure 7 indicates that this should also be the case for 14Nspin-labels since x- y motion does not modulate the resonance condition except in the central portion of the spectrum. Sensitivity of 14Nlabels at X-band microwave frequencies to x-y motion would thus be expected to be confined to the region of the V,’ spectrum where the spectral amplitudes C and C‘are routinely measured. Robinson and Dalton’ have examined the sensitivity of calculated outof-phase first harmonic dispersion signals (U,’) to x-y motion and have given a detailed description of the regions of overlap of the three nuclear manifolds which define the C and C’ parameters. The parameter C is measured in the region defined by the x and y turning points for the +1 and 0 spin states. The parameter C’ is measured from the region of the spectrum which is dominated by the g anisotropy of the mI = 0 manifold and lies almost in the middle of the x and y turning points. The magnitude of C’in the V i response is therefore determined in part by the x-y motional rate and in part by the z-x rate. Sensitivity of this parameter to x-y motion has been observed experimentally by Marsh5from 5-doxylpalmitate intercalated into dipalmitoylphosphatidylcholinebilayers. In progressing through a pretransition of lipid chains at 25 O C , the value for rC obtained from comparison of C’/C with the isotropic model curves of Thomas et alB2 indicated a decrease in correlation time from lo4 to lo* s while L”/L and H’YH indicated almost no change in correlation time. Model system approaches for deconvoluting the dynamic information contained in C’/C into its individual components for cases involving complex motional processes have not been forthcoming. We would note that at present it appears that the most reliable method for extracting D , and D, from a 14N V i line shape would be by a simulation approach rather than through an isotropic model system analysis alone. Figure 7 shows two regions of the 15N Vl spectrum which are dominated by the x and y turning points of the f1/2 spin states. These regions are separated in field space from each other (for labels in polar environments) and bear a direct physical resemblance to the f l manifolds from l4N. Examination of the V i spectra within a given column of Figure 4 indicates that the I’ and I” regions which are intermediate between the x and y turning points of the -1/2 and +1/2 nuclear manifolds, respectively, vary directly with the correlation time for x-y interconversion. It is evident that the spectral shapes in these regions also depend on the parallel-perpendicular correlation time. Sensitivity to x-y motion can be improved by increasing the observational frequency to 22 GHz with 15Nspin-labels.
This is a direct result of the increase in x-y anisotropy of the -1/2 nuclear state from 5 to 12 G and the accompanying increase in signal-to-noise of this manifold due to the decrease in total anisotropy. There are some features of the -1/2 manifold from 15N at 22 GHz which merit discussion. We have shown that the low-field extremum in Figure 7 (middle) is near the x turning point. There is, however, spectral density in this region which arises from intermediate orientations. This is understood most readily by plotting the resonance position as a function of 19 and 4 (normal spherical coordinates) for rotation of the nitroxide in the magnetic field. The approximate resonance conditions for [15N]nitroxide spin-labels as functions of the spherical angles (e,@) and the observational frequency are given by the following equations: 22
(3) where geff= g,, sin2 e cos2 4
aeff =
[uxx2sin2 e cos2 $
+ gyysin2 9 sin2 4 + gzr cos2 e
+ uW2sin2 e sin2 9 + uZz2cos
8]1/2
The field positions for the turning points will be obtained by setting 8 = 0, $ = 0 for 2, 6 = 90°, 4 = 0 for x , and 6’ = 90°, 9 = 90° for y. As the spin-label is rotated from an orientation of Ho along the nitroxide x axis toward the z axis in the x ,z plane (y-axial rotation), the resonance position at first moves slightly downfield with angle due to the competition between A and g anisotropy. At some intermediate angle, g anistropy becomes the dominant term and the resonance position shifts to higher field values until it reaches the z turning point at 6 = 0 which is intermediate between x and y. As e is increased from 0 to 90° in the z-y plane (x-axial rotation), the resonance position moves slowly away from its value at 6 = Oo due again to the competing effects of u and g. Thus, maximum sensitivity to motions which lead to x-y nitroxide axis interconversions would be expected near the z axis turning point while maximum sensitivity to z-x would occur in the lower half of the manifold and z-y in the upper half. This leads to the conclusion that, although the -112 manifold of [15N]nitroxidespin-labels at 22 GHz appears very similar to the mI = 0 line from 14Nat X band, spectral diffusion of saturation and hence line-shape behavior would be expected to be quite different for the two cases. It should be recalled that the resonance positions for the mI = 0 line from 14N are determined from g anisotropy alone and therefore are monotonic functions of the spherical angles 6 and 4. In general, it will not be possible to make a unique assignment of motion to one spectral region for anisotropically diffusing molecules. One can, however, change the appearance of motion by varying the relative field values of the turning points by employing variable-frequency observation. In the present study, we have demonstrated that K-band measurements can be utilized to increase sensitivity to x-y motional processes with I5N spin-labels. Other frequencies will be useful for increasing sensitivity or quenching sensitivity to specific rotational motions. From eq 3 we see that at L-band microwave frequency (- 1 GHz) the x and y turning points are nearly coincident and therefore rotations which modulate these ( 2 2 ) Balasubramanian, K.; Dalton, L. R. J. Magn. Reson. 1979, 33, 245-60.
J. Phys. Chem. 1983, 87,367-371
magnetic interactions do not lead to spectral diffusion of saturation and hence the V i line shape shows no sensitivity to this motional process.' At approximately 16 GHz, the z and x turning points will be coincident for the -1/2 nuclear manifold giving rise to a region of the spectrum which will have sensitivity to z-x interconversion Cy-axial motion) quenched. At approximately 30 GHz, the z and y turning points will be coincident for the -1/2 nuclear manifold giving rise to a region of the spectrum where sensitivity to z-y interconversion (x-axial motion) will be quenched. We conclude that utilization of multiple microwave frequencies will make it possible to observe anisotropic motion in greater detail. By positioning the z turning point relative to x and y one can adjust the way in which different motional processes will compete and alter ST-EPR spectra. Qualitative or first-order analysis is possible by comparison of experimental spectra with isotropic reference spectra if the two are recorded at two or three dif-
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ferent frequencies which are meaningful in the context of the above discussion. Quantitative information can then be obtained with the aid of computer-simulated spectra. Our simulations suggest that, in order to ensure that the motion about the three principal axes is defined correctly, one must determine the relative angle between the diffusion tensor and the magnetic tensor. It may be possible that this restriction can be relaxed if spectra are recorded at a variety of microwave frequencies.
Acknowledgment. This work was supported by grants from the National Institutes of Health GM-07884 and the Muscular Dystrophy Association. A.H.B. and K.B. were recipients of fellowships from the Muscular Dystrophy Association. L.R.D. is a recipient of a Research Career Development Award. Registry No. GAPDH, 9001-50-7; [15N,2H]maleimide, 83803-37-6.
Molecular Orbital Study of the Protonation of DNA Bases Janet E. Del Bene Depafiment of Chemistry. Youngstown State Unlverslty, Youngstown, Ohio 44555 (Received: August 13, 1982)
Ab initio SCF calculations with the STO-3G basis set have been performed to determine the optimized structures of the neutral and protonated DNA bases, thymine, cytosine, adenine, and guanine. Single-point Hartree-Fock calculations at these geometries have then been carried out with the split-valence 4-31G basis set to obtain the protonation energies. The most favorable protonation sites are O4on the C5 side of the C4=0 group in thymine, N3 in cytosine, N1 in adenine, and N7 in guanine. A relationship exists between the nature of the highest occupied n orbital and the preferred protonation site in each base, but a correlation between n orbital energies and relative protonation energies is not found. Protonation leads to significant geometrical changes in the base, particularly in bond lengths and angles near the protonation site. Charge transfer to the proton occurs and is accompanied by polarization of the electron density of the base toward the protonation site.
Introduction Protonation of nucleic acid bases at various centers plays an important role in certain biochemical processes and has been the subject of extensive experimental studies and theoretical investigations. The first theoretical studies based on ab initio calculations used molecular electrostatic potentials derived from ab initio wave functions for the bases as a means of investigating protonation sites.lr2 The molecular electrostatic potential describes the interaction energy between the unperturbed base and the proton (viewed as an external point charge), the assumption being that the interaction is purely electrostatic. While these studies have provided some insights into protonation, they do not yield values of protonation energies, and they neglect the electron redistribution (charge transfer and polarization) and structural changes which accompany protonation. Two recent ab initio studies of the protonation of selected DNA bases3i4 employed the minimal STO-3G basis set for the calculations, which were per(1)R. Bonaccorsi, A. Pullman, E. Scrocco, and J. Tomasi, Theor. Chim. Acta, 24, 51 (1972). (2) R. Bonaccorsi, E. Scrocco, J. Tomasi, and A. Pullman, Theor. Chim. Acta, 36, 339 (1975). (3) A. Pullman and A. M. Armbruster, Theor. Chim.Acta, 45, 249 (1977). (4)P. G.Mezey, J. J. Ladik, and M. Barry, Theor. Chim.Acta, 54,251 (1980).
formed at either standard or experimental geometries for the bases. However, it has since been demonstrated that this basis set severely overestimates absolute protonation energies and fails to give consistent relative protonation energies.k8 Therefore, it seems appropriate at this time to investigate the protonation of the DNA bases at a higher level of theoretical treatment. In the present study, optimized STO-3G structures for the neutral and protonated DNA bases thymine, cytosine, adenine, and guanine have been determined. For the ions, various isomers in which protonation occurs in the plane of the base have been considered. Single-point Hartree-Fock calculations with the split-valence 4-31G basis set have then been performed at these geometries to evaluate the protonation energies. The results of this study are reported in this paper.
Method of Calculation Protonation energies have been computed as the energies of the reaction B + H+ BH+ as given by HartreeFock calculations with the 4-31G basis setg at optimized
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(5) H. Umeyama and K. Morokuma, J. Am. Chem. Soc., 98,4400 (1976). (6)J. E.Del Bene, J. Am. Chem. Soc., 100,1673 (1978). (7)J. E.Del Bene, Chem. Phys. Lett., 55,235 (1978). (8) J. E. Del Bene, Chem. Phys. Lett., in press. (9)W. J. Hehre, R. F. Stewart, and J. A. Pople, J. Chem. Phys., 51, 2657 (1969).
0022-3654/83/2087-0367$01.50/00 1983 American Chemical Society
