2914
J. Phys. Chem. 1993,97, 2914-2921
Motion in Nitroxide Spin Labels: Direct Measurement of RoGtional Correlation Times by Pulsed Electron Double Resonance Duncan A. Haas, Tetsukuni Sugano, Colin Mailer,' and Bruce H. Robinson' Department of Chemistry, University of Washington, Seattle, Washington 98195 Received: October 29, 1992; I n Final Form: January 27, 1993
A new experimental technique has been developed to measure directly the rotational rate of a molecule connecting two portions of an electron paramagnetic resonance (EPR) spectrum, by a method which is independent of any factors in the Hamiltonian (such as A or g tensors) or the particular mechanisms of relaxation. Perdeuterated [ ISNITEMPOLand CTPO in glycerol-water mixtures and spin-labeled hemoglobin were studied using the time domain technique of pulsed saturation recovery electron double resonance (SR-ELDOR) in the 0.1-lo-@ motional time regime. The signal from the SR-EPR experiment (in which the pump and observer frequencies are the same) consists of a multiexponential decay, the amplitudes of all of the components being of the same sign. The SR-ELDOR technique of pumping one spin manifold or orientation and observing at another changes the sign of the amplitude of one or more of the components of the decay. The electron spin lattice relaxation rate ( Tle-l),the nitrogen nuclear spin-lattice relaxation rate ( TI"-'),and the characteristicrotationalcorrelation rate ( T R - ~ ) are measured directly, and independently, using a multicomponent exponential global analysis method. It was not possible, in general, to separate the three desired rates from one another with SR-EPR experiments alone. Pooling the SR-EPR and SR-ELDOR decay curves spectra was essential for success.
Introduction Spin labels have found application in biological and medical scienceprimarily becauseof their ability toreport on the molecular motion. As examples, perdeuterated [ISNITEMPOL,'CTPO? spin-labeled hemoglobin ( ~ l - H b )and , ~ spin-labeled glyceraldehyde-3-phosphate dehydrogenase (sI-GAPDH)~have been used as model systemsundergoing Brownian isotropicrotational motion in the micro- to millisecond time range characterized by a correlation time, T R . When motion is studied on the micro- to millisecond time scale, saturation transfer electron paramagnetic resonance (ST-EPR) has been the method of ~ h o i c e .There ~ are many examples in which ST-EPR is used to study slow motion? primarily using 14Nspin labels. ST-EPR relies on the Zeeman field modulation used todetect the EPRsignal and thecompetition between the spin-lattice relaxation time T I ,and the motionally induced transfer of energy to and from the resonance position. Experimental ST-EPR spectra are then either simulated or compared with ST-EPR spectra from a reference system (such as [15N,2H,7]maleimidelabeled GAPDH in glycerol4of known correlation times. The rotational rates are indirectly inferred from continuous wave (CW-EPR) and ST-EPR data Motional information may also be obtained with continuous wave electron-electron double resonance (CW-ELDOR), originally pioneered by Hyde and co-workers:' By pumping one point in a spectrum and observingat another point, polarization transfer is detected. The technique has been applied by Stetter et ale8to nitroxides moving with T R between 10 ps and a nanosecond and by Smigel et ale9to nitroxideswith microsecond correlation times. From CW-ELDOR, one cannot estimate either TI, or TI, independently, only their ratio. However, CW-ELDOR is an extremely complex technique, and the results can be influenced by instrumental artifacts.1° In this paper we show that the correlation time can be obtained directly from SR-ELDOR experiments and by a very direct method which requires only a very simple interpretation of the decay rates to obtain T R . We studied T R between 0.1 and 10 ps because (i) there is no good CW-EPR method for 0.1 ps < T R < 1 ps and (ii) ST-EPR works Permanentaddress: Physics Department, University of New Brunswick, Fredericton, NB, Canada E3B SA3.
0022-3654/93/2097-2914~04.00/0
well in the range 1 ps < T R < 10 ps and therefore provides a check on our time domain results. In the time domain EPR experiment, the spins are subjected to a short pulse of microwave power, and the observed data are the time dependence of the transient relaxation after the pulsing. The rates of relaxation are functions of the motional process. Two types of time domain experiments exist: one monitors spin echoes (a coherent detection of the x- and y-components of the magnetization), and the other monitors saturation recovery (a detection of the polarization of the z-magnetization). Freed and co-workers" have applied electron spin-echo(ESE) methodology to study motion in liquids. Following a (goo-T180°-r-observe) pulse sequence, the echo height, as a function of the delay time T , yields the phase memory decay time ( TM) which can be related to TR. The technique has been extended to studiesof spin-labeled membranes and vesicles-showing changes in TM with temperature.I2 Freed13 has also developed the technique of Fourier transform EPR using multiple pulse techniques, based on the analogous NMR experiment. The variation of TMacross the spectrum can be directly obtained and related to motional models. Cross-relaxation from one manifold to another can also be measured. Rates are measured from the volumes of the main and cross-peaks in the 2-D display and not from actual decay curves. The second time domain technique is that of pulsed SR-EPR, pioneered by Huisjen and Hyde.I4 It has beenapplied toa number of systemsin liquids15J6and used to measure Heisenbergexchange rates and dipole4ipole relaxation rates.17 The Hyde groupla has used SR-EPR, in conjunction with CW-ELDOR, to measure lateral diffusion of 14Nlabeled lipids in bilayers. In the SR-EPR experiment the component of the response that is proportional totheobserveramplitudeis theSRsignal. Thepumpandobserver are set to the same frequency. In an SR-ELDOR experiment, the pump and observer frequencies are set independently, but with a well-defined frequency difference. SR-ELDOR has been used to directly measure both the electronic ( Tle-I)and nuclear ( TI,-^) spin-lattice relaxation rate^.'^-*^ Measurement of rotational diffusion with SR-EPR may be inferred from the mechanisms of these spin-lattice relaxation rates.20 Experimentally it has proved to be very difficult to obtain the rotational correlation time directly as one component of a SRQ 1993 American Chemical Society
Motion in Nitroxide Spin Labels
The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 2915 the magnetization around within a given manifold. In addition nuclear spin flips, occurring at rate TI, -I, move the magnetization from one manifold to the other without causing molecular reorientation. Regardless of orientation or manifold, the magnetization eventually relaxes to the lattice at rate Tle-I. The SR-ELDOR experiment measures the decay of the transient component of the z-magnetization, ( M z ( t ; v , 8 ) )where , v is the nuclear manifold (which is i 1 / 2 for 15N),and 8 is the orientation variable, asshown in Figure 1. Theevolution of the magnetization can be understood, qualitatively, by a simple population analysis treatment. The master equation is
I
El
n
-
Field Figure 1. Linear absorption EPR spectrum of spin-labeled hemoglobin illustrating the positions where SR-ELDOR experiments are performed and the dependence of the resonance positions of the magnetization on spin-label orientation (given by 0). The figure illustrates how T R and TI, processes lead to spectral diffusion, whereas TI,characterizes the true spin-lattice relaxation.
EPR decay curve. A pioneering SR-EPR experiment by Fajer et on spin-labeled hemoglobindemonstrates these difficulties. Fajer et al. realized the complicated nature of the relaxation and tackled it by defining a single parameter, called the spectral diffusion rate ( T S D - I ) to take account of spin diffusion effects. They assumed that the only contributor to TSD was a single TRdependent spectral diffusion mechanism. Biexponential decays were observed. The slower rate was identified with TI;^. The fasterdecayrate ( T S D - ~ )wasa weakfunctionof T R . Theseauthors used a qualitative theory of spectral diffusion to extract the T R from TSD. Estimates of TR were obtained which were reasonable for motional times longer than 5 ps but were not in good agreement for faster motion. This analysis did not take into account spectral diffusion arising from manifold hopping (the TI,process), and this compromised their analysis of the faster decay. Attempts in our laboratory using SR-EPR alone to measure motion were no more successful.22 In the work presented here we demonstrate that the observed decays are in fact a multicomponentmixtureof the three relaxation processes: Tlc-I,Tln-l,and T R - ~ .The multicomponent nature of the signal is difficult to determine from SR-EPR in which all exponential amplitudes have the same sign. However, a combination of SR-EPR and SR-ELDOR can be used to obtain all three rates unambiguously. Analysis of multiple data sets enables one to directly measure the correlation time connecting two spectral positions as it is the component of the multiexponential decay with rate TlC-l T R - I . The relaxation rates TI;^ and T1n-l are also direct functions of T R , ~ O and their particular values can therefore provide independent estimates of T R . The T R from the decaycurvesarecompared with the 71 fromviscosity/temperature data and from ST-EPR experiments as a further check on the accuracy of the technique.
+
Theory
Figure 1 shows an absorption CW-EPR signal when the correlation time is longer than 0.1 ps. The figure illustrates the dependence of the signal upon molecular orientation. Reorientation, characterized by a rotational correlation time, T R , moves
cM,(t;v,e))i
- D V , 2 ( M , ( w w (1)
whereDis theEinsteinrotationa1 diffusioncoefficient( D = 1 / 6 ~ R ) and Vo2is the angular Laplacian operator. The system is pumped with a weak selective pulse so that the spin system is excited in manifold vp and at orientation 8,. The observer frequency is set to manifold v, and at orientation 8,. The recovery signal then has the form
(Mz(f;vo,801vp,6p) ) = ( M , ( 0 ; ~ ~ , 6 ~ ) 1 +fvo,vpe-f/Tin) x (1
+ P,(cos(B,)) P2(cos(8p))e-'ITR+ H.o.T.)
(2)
where (Mz(O;vP,Bp)) is the initial magnetization at time zero, when the pumping is completed and (Mz(r;vo,8,,~vp,8p)) is the magnetization at the observer position subject to the condition that all of the magnetization was at the pump position at time zero. P2(cos(8)) = (3 cos2(8) - 1)/2 and is the 1 = 2 component of the Legendre polynomials P,(x);fy,,,)= 1 if v = Y' and& = -1 if I = -v' (which is the case of going from one manifold to the other). This result assumes a short duration pump time, a low observer amplitude, and that the higher order terms (H.O.T.) from the rotational functions are not significant.23 Equation 2 predicts that one will observe four exponentially decaying componentswith the rate of each component a linear combination of Tle-l, TIn-',and T R - ~ . ?"le-' appears as a rate by itself and as an additive term to all other rates. T R appears in an exponential decay with a rate T R - I + TIe-I,and T I ,appears as a decay of rate Tl,-I TlC-I.The fourth component has rate TR-! TI"-! TIC-].Suitable positions of pump and observer can be chosen so that the signs of the individual amplitudes of the components of a decay curve containing both T I ,and T Rcan be changed, enabling analysis to disentangle the rates. For example, the amplitude of thecomponentscontaining Tln-lmay be switchedin sign by placing the pump and observer positions in different spin manifolds (fy,y~ = -1). The amplitude of the components containing ~ 1 - may l be switched in sign by setting the pump and the observer to different ends of the same manifold and changing the P~(cos(8)) term. A summary of the predicted signs of the amplitudes of the four exponentiallydecaying componentsis given in Table I. These simplistic equations predict that at the "magic angle" (8 = 5 4 O ) the 1 = 2 component will vanish so hence a pulse experiment at that spectral position will have no T R - ~component (the next higher motional term-the 1 = 4 component-will have rate 3 . 3 / T R and a smaller amplitude). These equations are not robust enough to include the case of pump and observer at different positions on one side of the magic angle within the same spin manifold.4.23
+
+
+
+
+
Experimental Procedure The 9.3-GHz (X-band) pulsed EPR spectrometer for these studies follows published design^.^^^^^ The spectrometer has three microwave arms-pump, observer, and detector bias. The observer and bias arms act as a conventional high sensitivity spectrometer for both linear EPR and ST-EPR experiments. The difference frequency between the pump and observer klystrons
2916 The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 TABLE I: Predictions Based on Equation 2 of Amplitude Si- Associated with the FdlorP.ing Rates: R1 = Z'le-I; R2 = Z'Ic-1 + ~ a - 1 ;R3 = 7"lc-' + 2 '1.~~; R4 = Z'lc-l + T R - ~ + TI.-'' obseNe/Dumv
A
B
C
D
R1 (-) R2(-) R3(-) R4(-)
R1 (-) R2(+) R3(-) R4(+) R1 (-) R2(-) R3(-) R4(-)
R1 (-) R2(+) R3(+) R4(-) R1 (-) R2(-) R3(+) R4(+) R i (-) R2(-) R3 (-) R4(-)
R1 (-) R2(-) R3(+) R4(+) R1 (-) R2(+) R3(+) R4 (-) Rf (-) R2(+) R3 (-) R4(+)
~~
A
B
C
R1 (-1 R2 (-1 R3 (-1 R4 (-)
D
Thelower halfis symmetric with theupper half. Thespectral positions A-D are defined in Figure 1.
LL
0.2
0.0
t I . I . I . I . I . I 0
20
40
60
80
100
FREOUENCY OFFSET (MHz)
Figure 2. Plot of I-mm loop gap resonator bandwidth. The data are the relative heights of the FID of a 1 mM solution of PADS (peroxylenedisulfonate) in saturated potassium carbonate solution produced by a 100-ns pulse of rf power on the resonator a t the frequency offset from LGR resonance as indicated on the abscissa. The solid line is the relative rf field amplitude produced by a resonator with a Q of 300.25
is phase locked to a low frequency (MHz) oscillator; moving the pump position to accommodateSR-EPR and various SR-ELDOR experiments is therefore both quick and easy. For free induction decay (FID) measurements the frequency difference is set to zero and no observe power is incident on the sample. SR-ELDOR operation is much simplified by the use of a loop gap resonator (LGR)26insteadof a bimodal EPR cavity. Sampleconcentrations were 1 mM or less. The Q of the LGR is approximately 300 which gives a 3-dB resonator bandwidth of 30 MHz (see Figure 2). At the 6&70 MHz offset often used for the SR-ELDOR experiment, the rf field in the resonator is about 5096 of maximum (Figure 2). The small size of the LGR produces a high power density leading to high rf fields for moderate powers (less than 1 W). Typical experimental conditions were pump power of 250 m W ,observer power of 100 pW, dead time of 80 ns, and acquisition time of 2 ns/point (or longer) for 1024 points. The pulse repetition rate was about 3 kHz. For our instrument the noise figure is 7 dB greater than the Johnson thermal noise voltage from the 5 0 4 input resistor of the low noise microwave amplifier; the system base-line noise is only a factor of 2 greater than the theoretical limit.25~27 SR-EPR and SR-ELDOR are both polarization experiments which measure the recovery of the system to equilibrium. A selectivepulse is applied to the spins which alters the polarization and burns a partial hole in the absorption line. In SR-EPR, the frequency of observation is essentially indentical to the pump's and the signal is a pure recovery as the polarization spreads
Haas et al. throughout the spin system and out to the lattice. In SR-ELDOR experiments, the frequency of the observer and pump are very different and both the arrival and decay of magnetization are observed. It is neither necessary, nor desirable, for the pump to be coherent with the observer. The experimental decay curves are obtained using various pump times and pumpobserver frequency differencesas described below. The pump timecontrols the relative amplitudesof thevarious componentswhichcontribute to the overall relaxation of the magnetization, and the p u m p observer frequency difference controls the signs of the amplitudes of the exponentiallydecaying componentsin ways approximately predicted by eq 2 and summarized in Table I. The FID docs not pose as great a problem here compared to the fast motion regime (where the FID has roughly the same rate as Tle-l and Tln-I). FID effects are minimized, though, by (i) using r pulses (or multiples thereof), (ii) having the pump klystron frequency not coherent with that of the observer klystron (for SR EPR experiments,a small frequencydifferenceof 350 kHz was used), and (iii) inverting the phase of the observer field for half of the scans and subtracting, which cancels out the phase-independent FID (and digitizer coherent noise). In some cases a small FID remained, as predicted theoretically by Percival and Hyde.2*By insertion of a piece of metal into the Zeeman field to decrease the field homogeneity, the FID decay rate could be increased to a point where it easily could be distinguished from the rates of interest (or be short enough to be lost in the 80-11s dead time). Background subtraction was used to further reduce spurious coherent signals-switch transients, etc. The off-resonance field position for the observer was placed over 100 G away in the direction such that the pump's location is even further off resonance (to ensure that there was no signal response in the background acquisition). The decay curves shown in Figure 6 have a signal-to-noise (SNR) ratio of approximately 40:l and are the result of 60 OOO scans on resonancesubtracted from 60 OOO off resonance. They took about 1 min to obtain. The time to acquire a singledecay curve was a compromise between obtaining the best SNR and getting a complete set of data for the linking and pooling analysisprocedure described below. The temperature stability of the match of the,LGR resonator to the coaxial line was also a long-term limitation as drift of this could cause the signal to shift out of the range of the digitizers. If extremely long signal averaging is done (>30 min), there are indications of coherent noise from the Biomation digitizer that would eventually limit SNR despite base-line subtraction and phase modulation. Usually eight decay curves were obtained for a complete set of data-two with different digitizer rates (e.g. lOand 20 ns/point, see Figure 6) at each of four field positions (e.g. SR-EPR at B, and SR-ELDOR with C-B, E A , and A-C positions as defined in Figure 1). The rotational correlation time of the spin label is determined in two independent ways to calibrate the results of the pulsed experiments: (i) from thestokes-Einstein (S-E)expression, using known solvent viscosity and the temperature, and (ii) from STEPR spectra (for T R = 1 p s or longer) using the L"/L ratio of the signal heights from spin-labeled GAPDH.4 T R is proportional to the ratio of viscosity ( v ) to absolute temperature by the Stokes-Einstein equation: T R = V(v/keT). The constant of proportionality is the molecular volume, V = 4 / 3 d , where r is the molecular radius and k~ is the Boltzmann constant; all quantities are in cgs units. The molecular radius of sl-Hb was taken to be 29 A, and that of TEMPOL to be 2.2 A. Thisvalueofr = 2.2A in theS-Equationgavethebestagreement with T R calculated from linear CW-EPR line widths; it is in the range predicted for r for this spin label by Hwang et alaz9The glycerol-water solutions were 80% glycerol by weight for the TEMPOL and CTPO samples and 60%glycerol by weight for sl-Hb. Experimental data of viscosity (7, in centipoise) versus absolute temperature and percent glycerol were least-squares
-
(n
The Journal of Physical Chemistry, Vol. 97,No. 12, 1993 2917
Motion in Nitroxide Spin Labels
TABLE 11: Constants Used for Modeling the Dependency of Parameters A md B on the Percenta e of Glycerol ( X ) in the Equation for Viscosity In q = A + B$'P Determined by I-east-Squrrres Fit of the Following Functions Based on Experimental Viscosity Measurements:j'J1
+
A = Jo
(
-2.4322 6.042 X
K
'02
10'
)
'
B = KO+ K,X + KrU2
0
parameter
J
J'x
1+J*
2
3
6X10-8 -1.415 X lo4
3.5 229.09
1
lo7
0.01165 7.514 X
lo5
+ K3X3
: lo2
h
; 10'
1
IO-^
lo-'
IO-^
10-~
lo-'
loo
lo-* 10-~
CORRELATION TIME (sec)
Figure 3. TI;' for TEMPOL (filled squares) and sl-Hb (open squares), Tln-lfor TEMPOL (filled triangles) and sl-Hb (open triangles), and T R - I estimated from the recovery rates for TEMPOL (filled circles) and for sl-Hb (open circles; see Figure 6 for typical data) obtained from multiexponential fits to SR-ELDOR data sets. The rates are plotted as a function of the rotational correlation time, T R , calculated from viscosity and temperature data via the Stokes-Einstein equation (for T R < 1 M) and from ST-EPR spectra (for T R > 1 ps) as shown in Table 111. The solid upper straight line represents T R - ~vs T R to illustrate how the circles compare with the ideal case. Superimposed on the T1n-l and TI;' results are the theoretical fits from ref 20. CTPO results (TI;'(open diamond), TI.-^ (open inverted triangle), and TR-' (filled inverted triangle)) are also included.
+
fit to In q = A B/ p. For conveniencein calculating theviscosity at any particular temperature or percent glycerol, the dependence of the A and B parameters on the percentage of glycerol ( X ) was found by least-squares fitting theviscositydata3OS3Ito the following functions: A = JO JIX/( 1 + JfiJ3) and B = KO KIX KzX K#, where the Ji and Ki are constants given in Table 11. In Figure 3 the relaxation rates found by SR-ELDOR are plotted against T R values determined by this viscosity method for T R faster than a microsecond. For slower T R the temperature required is well below the freezing point of the glycerol solutions, so rather than extrapolate the S-E equation, ST-EPR data (which are more applicable to systems with T R longer than a microsecond) were used to estimate T R . The ST-EPR spectra were recorded immediately before or after the time domain experiments. An example of an ST-EPR spectrum for TEMPOL, with a simulation overlaidon the data, is given in Figure 4, with the spectral positions LNand L indi~ated.~ The ST-EPR and CW-EPR spectra (data not shown) for TEMPOL were simulated using well-established procedures.32 Table I11 shows the estimates of T R , based on the S-E relation and the ST-EPR spectra, along with the values obtained directly from SR-ELDOR experimentsdescribed below. The fundamental limit to the measurement of long correlation
+
times is the magnitude of TlC-l;the Tlc-l + TR-I decay rate tends to TlC-Ias the correlation time slows and eventually will become indistinguishable from it. The fastest correlation time which can be convenientlymeasured is 30 ns; this is a practical, experimental limit because the decays have low amplitudes and are lost in the dead time (80 ns). The SR-ELDOR experiment proceeds as follows: For a given value of T R the field positions of the pump and observer are set, and a number of decay curves over different time scales are obtained. The data sets are, in principle, identical, except for a base-line offset and the times at which the data are sampled. Therefore, we define these decays to be linked; the linked data sets are acquired with respect to a common time origin, which is at the end of the pump period. Obtaining data on different time scales is helpful, because the global analysis fitting routine is more stable when it is provided with both a high density of points closer to time zero (which aids in determining the faster rates) and some data points over a longer time (which measures the slowest rate, always TlC-l). Sets of linked spectra are then collected under different experimental conditions: e.g. changing the pulse length changes the relative amplitudes; changing the pump and observer field positions changes the signs of the individual components of the decay. If field positions B and C (see Figure 1) are used, then the amplitude for the component involving Tln-l is positive and that for TR-I is negative (see Table I). The situation is reversed when field positions A and B are used. The component which relaxes at rate Tlc-l is always negative. The spectrometer's field marker positions (A-D) were selectedusing the features of theintegrated linear CW-EPRsignal (such as in Figure 1). If the turning points are not well defined, however, these positions can be difficult to assign, and there is also uncertainty about the exact position of the magic angle. If one attempts an A-to-B experiment but the magic angle point is accidentally used for either the pumping or observing position, the rates involving ~ 1 - are l suppressed and the decay curve looks much like that of an SR-EPR experiment. Because the highfield manifold is at least three times wider than the lower one, working with positions C and D avoids this potential problem, although the weaker signal requires longer periods of signal averaging. Manifold overlap is greater for 14Nspin labels than with the I5N labels used here. Manifold overlap is not a problem for we have a wide choice of field positions for the ELDOR experiments that always will allow clear separation of the leaving and arriving positions no matter which isotope is used. All sets of linked data are thenpooled within the global analysis fitting routine, with the amplitudes of each component within a linked set the same. This technique, an application of global analysis, is well recognized in optical spectroscopy as being extremely effective in determining relaxation rates."
+
+
+
Data Analysis We define X? to describe the quality of either a theoretical fit to an N data point curve or of the overlap between two linked data sets (N is then the number of points with common time values) as
where Yl is the first data set, Y2 is either the theory or a second data set, Y is the number of constraints used to fit the two sets, and the standard error for the noise for data set j is
For data sets, unj2is calculated by fitting a single exponential to the tail end of a background (off-resonance) acquisition for set
2910 The Journal of Physical Chemistry, Vol. 97, No. 12, 1993
Haas et al.
f“ M
i
i
Figure 4. ST-EPR spectrum (second harmonic, quadrature signal) of 1 mM TEMPOL in a 90% glycerol solution at -34 OC. The data are overlaid with a simulation (dot-dash line) with an input value for TR of 1 p. The simulation also included an additional nuclear relaxation time (TI.*) of 1.7
which represents the difference between the predictions for ?‘In based on the END mechanism (already included in the calculationm) and the experimental results (see Figure 3). The Zeeman modulation frequency was 50 k H z with a peak-to-peak amplitude of 5.0 G. Under nonsaturating conditions, the signal phase angle was set to null the quadrature signal.34 Data acquired with 1-mW observer power was rotated to the same phase angle, and the quadrature spectrum is shown. The spectral positions used for estimating TR,L”and L4 are indicated on the plot. The parameters used in the simulation were gxx = 2.008 34, g, = 2.005 75, grr = 2.0020; A, = 9.76, AyY = 9.45, A , = 50.32; TI,= 25 ps, 7‘20 = 25 M, Tin* = 1.7 js; T R = 1 ws; and microwave field amplitude hl = 0.14 G. ps
TABLE IIk Values for T R (in microseconds) Calculated Using Various Methods: (a) Stokes-Einstein Equation (q/Z); (b) Value of T R Used as Input io the ST-EPR Liw Shrpe Simulation Program Which Cave Best Fit of Theory to Experiment; (c) Determination Based on ST-EPR Amplitude Ratio L”/L,Calibrated with CAPDH‘ (Valid for T R = 1 ps or Longer); (d) Multiexponential Fitting of SR-ELDOR Decay Curves (This Work) TU
TEMPOL TEMPOL TEMPOL TEMPOL TEMPOL CTPO SI-Hb SI-Hb
method a
method b
0.16 0.30 1.4 8.4 9.3 5.9 1.1 1.5
0.1 0.2 1.o 5.0 7.5
method c
method d
1 5 9 6 4 4
0.15 0.25 0.6 5.8 5.5 8.6 3.0 3.1
j . The factor of 2 in eq 4 accountsfor the fact that the experimental
curve is the difference of the on- and off-resonance sets. (When Y2 is a theoretical fit, unz2equals zero because a model curve is noise free.) The values of x?, for the overlap of linked data sets, as well as a visual inspection of the linked data, provide a good indication of experimental reproducibility; if x> is not of order unity, then the data sets are not truly reproducible. Having data sets linked together reduces the size of the computation involved because only a single least-squares best fit model is obtained for the entire linked set. Moreover, the results of the analysis are consistent with the predictions of eq 2 and Table I. Onceone hasobtaineda uniqueset ofdecay rates that minimizes the global xr2of the fit (which is the sum of the individual values
of x,*), one must identify the processes which give rise to each individual decay rate, viz., whether it is due to Tt,-I, Tln-l, or rotation. A suitable choice of experimental conditions for acquisition of the decays enables the rates to be distinguished. The strategies we have found useful are as follows: (i) A pump time that is long compared to the relaxation time of a particular component will tend to suppress the amplitude of that component. (ii) Pumping and observing at the magic angle (6 = 5 4 O and Pz(cos(0)) = 0) will reduce the amplitude of the motional rate leaving mostly those rates involving Tl,-l and T1n-l. (iii) Pumping in one spin manifold and observing in the other will always invert the amplitude of the ( T d + T1n-l) decay curve. (iv) Pumping at one extreme turning point of a spin manifold and observing at the other will invert the amplitude of the ( Tle-I + 71-l)decay curve. (v) Pooling the SR-EPR and pulsed ELDOR decay curves for analysis is essential for all rates to be found; neither experiment alone is sufficient. The fitting routine is stabilized during the early stages of the fitting process by using fixed values for TI$-^ and/or T1n-I obtained using procedures i and ii. Each cycle of the Marquardt/gradient search predicts an adjustment to the rates and coefficients to improve the fit. The matrix problem is constructed in such a way that some of the relaxation rates may be held fixed and all other variables may be simultaneously adjusted. When the process begins to converge, Tle-l and/or Ttn-lrates can then be floated for best final fit. These strategies were developed after it was found that the TEMPOL data sets acquired in the microsecond range are composites of four exponentials whose rates lay within an order
Motion in Nitroxide Spin Labels
The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 2919
-
of magnitude of each other. In such a case it became impossible to uniquely (or reliably) fit an isolateddata set. Either the fitting routine became unstable or, as was often the case, two of the rates came very close together with their amplitudes roughly equal but opposite in sign. In the latter case, it is important to know whether this result is correct or just an artifact. The procedure outlined above solves these problems for a number of reasons. The larger volume of data stabilizes the fitting routine. A short dwell time experiment provides necessary information for determining the fast rates but offers little information for the slower rates. Finally, the predictionsconcerningthe signsof theamplitudes, summarized in Table I, establish strict criteria for judging the physical reasonableness of the fits.
0.050
2
,
We have obtained relaxation rates Tlc-l and TI,-] from perdeuterated [ ISNITEMPOL in glycerol-water mixtures over the T R range from 0.05 to 250 ps. Within the center of that range, the correlation time was also measured as one component of the relaxation curves. Biexponential recovery curves were obtained from the SR-ELDOR data when the magic angle was chosen for the pumping and observing positions (as shown in Figure 1). The use of deuterated labels does not affect the methodology of theseexperiments, except that the SNR is usually better with deuterated labels. In Figure 3 are plotted the TI*-I and Tln-l rates versus correlation time in the slow motion range. The very weak dependence of Tle-l on correlation time goes as 1/TR1/*(bottom line in Figure 3) and is discussed elsewhere.20 The upper curved line in Figure 3 is the theoretical dependence of T1n-l on T R predicted by the electron nuclear dipolar mechanism as developed elsewhere.20The amplitudes of all the components changed sign as predicted in Table I. Within the motional range from to 1od s the Tln-l rates are a very strong function of the motion and uniquely determine the correlation time. The sensitivity of Tln-l to the motion complements nicely both the CW-EPR and ST-EPR techniques in this motional regime where neither is particularly sensitive to correlation time. Explanations for the slight deviation of the experimental data from the theory may lie in the presence of oxygen or additional small paramagnetic interactions (such as from spin-spin concentration effects, etc.). We should emphasize that whatever the reasons for the particular values of TIC-'or Tln-l found in the experiments they are irrelevant to the use of this method to obtain T R . It is well-known that the measured value of TI;' contains a term which is proportional to the observer p o ~ e r . 2 ~The dependence of Tle-I and TI,,-^ upon observer power level was investigatedexperimentally. At a number of observer power levels, the results of an SR-EPR experiment (pump time 25 ps, dwell time 100-200 ns/point) were pooled with a cross-manifold ELDOR experiment at the magic angle (pump time 300 ns, dwell time 50 ns/point). The data at all observer levels were fit very well with two exponentials. The results, overlaid with linear regression fits, are plotted in Figure 5 as relaxation rates vs
0.043.
0.033
0.28
0.030
10.26
I 0.1
0.2
0.3
0.16 0.30 1.4 8.4 9.3 5.9 1.1 1.5
5.25 X 5.01 x 3.97 x 3.86 X 3.83 x 3.74 X 9.37 X 6.52 X
10-2
10-2
le2 10-2
It2 le2 le2
6.78 4.02 1.59 0.212 0.219 0.153 0.421 0.384
'
0.4
0.24
OBSERVER POWER (milliwatts) Figure 5. Dependence of TI;^ (squares, left axis) and Tln-l(triangles, right axis) in megaradians/second on observer power level in milliwatts for a 1 mM sample of TEMPOL in 90% glycerol solution at 4 4 O C (correlationtime was 5 ps). Therates weredeterminedby pooling together SR-EPR and magic angle ELDOR experiments and fitting them to rates TI;^ and TIn-'+ TI^-'. Overlaid on the data are linear regression fits. For TlC-l, the slope m f 2um = 0.044 f 0.0052 (Mrad/(mW s)), and the intercept b f 2Ub = 0.0302 f 0.0011 (Mrad/s). For Tl,,-I,m f 2um = 0.052 0.082 (Mrad/(mW s)) and b 2Ub = 0.3303 f 0.017 (Mrad/
*
*
SI.
microwave observer power. The slope of the Tl,,-l results is essentially zero (the error in the slope of the fit is greater than the slope itself); there appears to be no significant observer effect on Tln-l. For Tlc-I, there was a 16% increase at 0.1 mW (the power level used in most experiments) compared to the extrap olated value at 0 mW, which was not corrected for in the tables or figures. In the TR = 0.1-10-ps range, the CW-EPR absorption line shape has the shape shown in Figure 1. In this motion time range the effects of motion now become evident in the recovery curves; they can no longer be fit satisfactorily with just two exponentials. According to eq 2, there should be at least four rates present. Experimentswere performed by employing strategiesi-vdescribed above, and the curves were fitted with either three and four exponentials, using global analysis. For the TEMPOL data in the microsecond range, the X? of the fits involving four rates were always a 10% or more improvementover those with three rates. At the fastest correlation times, the fourth rate was lost in the dead time. From the rates determined by the fitting, and knowing the signs of the amplitudes ofeachofthecomponents, Tlc-l,Tln-',and 7R-I canbecalculated and identified. In the experiments on sl-Hb and CTPO the X? of the data fit to three rates did not improve when a fourth rate was added. This is because the data sets did not include enough recoveries acquired with a very short dwell time. These results, summarized in Table IV,for TEMPOL, CTPO, and sl-Hb are plotted in Figure 3. The effect of the motion on the shape of a relaxation curve is visually most apparent in the case of sl-Hb. The SR-ELDOR curves from the TEMPOL experiments all had the same basic
TABLE I V Rates (megaradians per second) from Figure 3 for I?its Involving T R (in the 0.1-10-rs Range)' d t l / T) R1 = TIe-' R2 R3 R4 T1n-l TEMPOL TEMPOL TEMPOL TEMPOL TEMPOL CTPO SI-Hb d-Hb
0.40
0.047 .
1
0.0
Results and Discussion
I
4.50 2.97 0.993 0.311 0.264 0.414 2.08 2.83
2.54 0.479 0.446
4.45 2.92 0.953 0.272 0.226 0.377 1.98 2.77
TR(fitj
~
0.15 0.25 0.6 5.8 5.5 8.6 3.0 3.1
a T R ( p )in column 2 is calculated from solvent viscosity ( 7 ) and temperature, and TR (11s) in the last column is calculated from fits to time domain experiments. R2 = TI.-^ in all cases, but the rates R2 and R3 are not necessarily in simple ascending order; rather, they are as defined in Table I, on the basis of the signs of the amplitudes of these components. and T R (fit) are calculated from the equations in Table I.
2920 The Journal of Physical Chemistry, Vol. 97, No. 12, 1993
Haas et al.
shape, so that one could not distinguish the intermanifold from the intramanifold experiments without some knowledge of the magnitudes of the Tln-Iand rR-related rates. The ELDOR experimentswith sl-Hb, on the other hand, yielded clearly different shapes for the intermanifold and the intramanifold experiments. This is possibly because the rates were better separated in value compared with the corresponding values for the TEMPOLglycerol system. Figure 6 shows examples of the SR-EPR and SR-ELDOR data for sl-Hb tumbling in the 1-5 FS time range. Each plot consists of two linked curves, differing only in dwell time. Superimposed on each of the data sets is a least-squares best fit simulation composed of three exponentials and a base line. The top curve is the SR-EPR data acquired at point B (defined in Figure 1). This curve is a simple recovery and all components have the same sign (see Table V). The bottom curve (SR-ELDOR from C to B) is the data when the pump is set on C and the observer frequency is set to B. This represents a jump from one manifold to the other, and the amplitude of those components which contain Tln-l in the rate change sign (Table I). The middle trace of Figure 6 (SR-ELDOR from B to A) is the data for the pump on B and the observer on A. This corresponds to the pumpobserve case within a manifold. In this case the amplitude of the components containing TR in the rate will change sign, and this shows up clearly as a dip in middle of this SR-ELDOR curve. TableVI illustrates that the residual x?of the three-exponential fit for individual data sets is the same as the X? describing the overlapof linked data sets (either as repeat runsor as data acquired using a different dwell time); this means that the uncertainty of the fit is within the uncertainty of the data reproducibility and cannot therefore be improved further. The rates of the three exponentials are the same for all data sets, and the amplitude signs are consistent with Table I. Table V also lists rates for a group of data sets acquired using positions A and C (data not shown). The values of TlC-l, Tln-I, and Q-I, calculated directly from eq 2 with a 10%error estimated by the fitting process, are plotted in Figure 3 for TEMPOL, sl-Hb, and CTPO, and are summarized in Tables I11 and IV. The quality of the results can be judged by inspection of Table 111. At faster motional times, the rotational correlation time measured by SR-ELDOR of the TEMPOL samples is in excellent agreement with the nominal correlation time determined from solvent viscosity and the hydrodynamic radius. In the microsecond range, the SR-ELDOR results are in most cases in good agreement with the L"/L ratio from ST-EPR calibration data. We must note that SI-GAPDH was used for reference in the ST-EPR calibrations4 while the actual experiments were done with SI-Hb;it is quite possible that the differences in T R in the last two rows of Table I11 arise from this.
Conclusions We have measured the values of the electron and nuclear spinlattice relaxation times in the ultraslow motion region using SRELDOR and SR-EPR and find that the measured values of Tic-' depend on 1/ r ~ ' a/ ~ power , law dependence which is consistent with a model of spin diffusion in liquids.20 Note that for spin labels moving in the lCL1000-nsrange Tln-Iis much greater than Tlc-l (an unusual situation, contrary to NMR experience). This is primarily due to the ability of the electron in this particular rotational range to efficientlyrelax the nucleus, while the electron has only the much weaker nuclear spin to relax it. If SR-ELDOR with SR-EPR is used and then the data acquired are pooled by using different pump and observer field positions, the rotational correlation time can be measured directly; it is seen experimentally as a single-exponential component of the relaxation. This experiment is the first time rotational motion has been quantitatively measured as a single-exponentialdecay. We hope it will be possible to directly measure rotational
. .-
t 1, ,'3
.'i ,
. . . s.a . . . . . I . . . i.8 . a. . L . .a. . , ?I* t:& Mpw 6. Three different plots of SR-ELDOR spectra of sl-Hb, taken at different pump and observation positions. Each plot includea twodata sets, acquired using differentdwell times, which have been linked together (data sets are brought to a common base line by minimizing the xr) of overlap; linked sets have the same amplitudes and rates). The top curve is the SR-EPR spectrum at position B (see Figure l), the middle curve is the SR-ELDOR spectrum pumping at position B and observing at position A, and thebottomspectrumis theSR-ELDORspearumpumping at position C and observing at position B. Superimposed on each pair of spectra is the least-squaresbest fit consistingof an adjustable base line and three components, each of which is a single-exponential decay (see cq 2). The rates and normalized amplitudes are given in Table V, and the rates are included in Figure 3. R'*.
,
. Ut" . .
;l
.o
I
I
I
;Io'
I
Motion in Nitroxide Spin Labels
TABLE V Hb Fit.
The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 2921
Rates and Relative Amplitudes for Spin-Labeled amplitudes
ELDOR
SR rate type
rate (Mrad/s)
AvrO, A8=O B- B
Rle R l e 1/71 Rle + Rln
6.516X 3.840 X I t ' 2.834
-1.193 -10.63
+
-1.ooO
Av= 1, A v r O , AB=O A 8 = 9 0 C - B B-A
Av= 1, A8=90 C-A
4.321 4.272 +1.122
4.332 +O.2oO +0.395
-1.299 +0.079 -1.586
* Spectral positions A - C are defined in Figure 1. Amplitudes are relative to the amplitude of the slowest component of S R (Rle); base lines are not shown. TABLE VI: Quality of SI-Hb Fit and Data Overlap. expt type dwell time (ns/point) X? fit xr2data Av 0, A8 0 Av = 0, A8 = 0 Av = 1, A8 = 0 Av=l,AB=O Av = 1, A8 = 0 Av = 1, A8 = 0 Av = 0, A8 = 90 Av = 0, A8 = 90 Av = 1, A8 = 90 Av= 1 , A 8 = 9 0
20 10 20 20 10 10 20 10 20 20
1.14 0.92 1.46 1.26 0.87 0.93 1.07 0.69 0.99 1.10
0.92 1.09 1.13 1.19 0.74
1.01
See Figure 6 and Table V. X? data is the xr2comparing two data sets taken with different digitizer dwell times but otherwise identical. x? fit is the xr2comparing a single data set with the best least-squares fit to a model set of rates.
reorientation by pulsed SR-ELDOR in systems characterized by anisotropic motion. These types of time domain experiments are a necessary underpinning of and improvementon traditional CW techniques. Quantitative simulation of ST-EPRspectra invariably requires knowledgeof the tensorial interactions and the relaxation rates of the spin system. Direct measurement of TI;' and TI"-' with pulse techniques is clearly superior to performing progressive saturation studies using CW-EPR.
Acknowledgment. We gratefully acknowledge thegiftsof 15Nspin-labeled hemoglobin from Dr. P. Fajer and of perdeuterated CTPO from Dr. H. Halpern. This work was supported by National Institutes of Health Grant No. GM32681 and by the Natural Sciences and Engineering Research Council of Canada. References and Notes (1) Dalton, L. R.; Robinson, B. H.; Dalton, L. A.; Coffey, P. Saturation Transfer Spectroscopy. In Advances in Magnetic Resonance, Vol. 8; Waugh, J. S., Ed.; Academic Press: New York, 1976; pp 149-259. (2) Halpern, H. J.; Peric, M.; Nguyen, T.; Spencer, D.; Teicher, B.; Lin, Y. J.; Bowman, M. K. 1. Magn. Reson. 1990, 90,40-51. (3) Thomas, D. D.; Dalton, L. R.; Hyde, J. S. J . Chem. Phys. 1976,65, 30063024. (4) Beth,A. H.; Robinson, B. H. Nitrogen-1 5 and DeuteriumSubstituted Spin Labels for Studies of Very Slow Motional Dynamics. In Biological
Magnetic Resonance VIII Spin Labeling: Theory and Application; Berliner, L. J., Reuben, J., Eds.; Plenum Press: New York, 1989. ( 5 ) Hyde, J. S.; Dalton, L. R. Chem. Phys. Lett. 1972, 16, 568-572. (6) Hyde, J. S.;Dalton, L. R. Saturation Transfer Spectroscopy. In Spin Labeling: Theory and Applications; Berliner, L. J., Ed.; Academic Press: New York, 1979; Vol. 11. Chapter 1, pp 1-70. (7) Hyde, J. S.; Chien, J. C. W.; Freed, J. H. J . Chem. Phys. 1968, 48, 421 1-4226. (8) Stetter, E.; Vieth, H. M.; Hauser, K. H. J. Magn. Reson. 1976,23, 493-504. (9) Smigel, M. D.; Dalton, L. R.; Hyde, J. S.; Dalton, L. A. Proc. Narl. Acad. Sci. U.S.A. 1974, 71, 1925-1929. (IO) Dalton, L. A.; Dalton, L. R. Modulation Effects in Multiple Electron Resonance Spectroscopy. In Multiple Electron Resonance Spectroscopy; Dorio, M. M., Freed, J. H., Eds.; Plenum Press: New York, 1979; Chapter 5.. DD .. 169-228. (1 1) Stillman, A. E.; Schwartz, L. J.; Freed, J. H. J . Chem. Phys. 1980, 73, 3502-3503. (12) Madden, K.;Kevan, L.; Morse,P. D.;Schwartz, R. N.J. Am. Chem. Soc. 1982,104, 10-13. (13) Gorcester, J.; Millhauser, G.L.; Freed, J. H. In Modern Pulsed and Continuous- Wave ElectronSpin Resonance; Kevan, L., Bowman, M. K., Eds.; Wiley: New York, 1990 Chapter 3. (14) Huisjen, M.; Hyde, J. S.Rev. Sci. Instrum. 1974, 45, 669-675. (15) Percival, P. W.; Hyde, J. S.J. Magn. Reson. 1976, 23, 249-257. (16) Kusumi, A.; Subczynski, W. K.; Hyde, J. S. Proc. Narl. Acad. Sci. U.S.A. 1982, 79, 1854-1858. (17) Steinhoff, H. J.; Dombrowsky, 0.; Karim, C.; Schneiderhahn, C. Eur. Biophys. J . 1991,20,293-303. (18) Yin, J. J.; Pasenkiewicz-Gierula, M.; Hyde, J. S.Proc. Narl. Acad. Sci. U.S.A. 1987, 84, 964-968. (19) Hyde, J. S.;Froncisz, W.; Mottley, C. Chem. Phys. Lett. 1984,110, 62 1-625. (20) Mailer,C.; Robinson, B. H.; Haas, D. A. New DevelopmentsinPulsed Electron Paramagnetic Resonance: Relaxation Mechanismsof Nitroxide Spin Labels. Bulletin of Magnetic Resonance; International Society of Magnetic Resonance: Vancouver, British Columbia, Canada, 1992; Vol. 14, pp 30-35. Haas, D. A,; Mailer, C.; Sugano, T.; Robinson, B. H. New Developments in Pulsed Electron Paramagnetic Resonance: Direct Measurement of Rotational Correlation Times from Decay Curves. Bulletin of Magnetic Resonance; International Society of Magnetic Resonance: Vancouver, British Columbia, Canada, 1992; Vol. 14, pp 35-40. (21) Fajer, P.; Thomas, D. D.; Feix, J. B.; Hyde, J. S. Biophys. J . 1986, 50, 1195-1202. (22) Unpublished experiments with Dr. P. Fajer. (23) Sugano, T. A Study of Very Slow Rotational Diffusion by SR-EPR. Ph.D. Thesis, University of Washington, 1987. (24) Mailer, C.; Danielson, J. D. S.; Robinson, B. H. Rev. Sci. Instrum. 1985,56, 1917-1925. (25) Mailer, C.; Haas, D. A.; Hustedt, E. J.; Gladden, J. G.; Robinson, B. H. J. Magn. Reson. 1991, 91,475-496. (26) Medical Advances, Milwaukee, Wis Loopgap Resonator Model No. XP-0201. (27) Horowitz. P.; Hill, W. The Art of Electronics; Cambridge University Press: Cambridge, U.K., 1980; Chapter 7. (28) Percival, P. W.; Hyde, J. S. Reu.Sci. Instrum. 1975,46.1522-1529. (29) Hwang, J. S.;Mason, R. P.; Hwang, L.-P.; Freed, J. H. J . Phys. Chem. 1975, 79, 489-5 1 1. (30) CRCHandbookof Chemistry andPhysics; CRC Press: Boca Raton, FL. 1965: Vol. 46. (31) Sehr, P. A.; Mailer, C.; Devaux, P. F. J . Magn. Reson. 1983, 52, 23-34. (32) Beth, A. H.; Balasubramanian, K.; Robinson, B. H.; Dalton, L. R.; Venkataramu, S. D.; Park, J. H. J . Phys. Chem. 1983,87, 359-367. (33) Beecham, J. M.; Gratton, E.; Ameloot, M.; Knutson, J. R.; Brand, L. In Principles of Fluorescence Spectroscopy; Lakowicz, J. R., Ed.; Plenum Press: New York, 1991; Vol. 2, ChaDter 5. (34) Auteri, F. P.; Beth, A. H.; Rbbinson, B. H. J . Magn. Reson. 1988, 80,493-501.
