Use of EPR To Investigate Rotational Dynamics of Paramagnetic

Tatyana I. Smirnova, Alex I. Smirnov, R. L. Belford, and R. B. Clarkson. Journal of the ... John W. Chen, Robert B. Clarkson, and R. Linn Belford. The...
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J. Phys. Chem. 1994,98, 13452-13459

13452

ARTICLES Use of EPR To Investigate Rotational Dynamics of Paramagnetic Contrast Agents J. W. Chen,**+9$F. P. Auteri,’ D. E. Budil? R. L. Belford$3* and R. B. Clarkson*~~ Department of Chemistry, Department of Veterinary Clinical Medicine, College of Medicine, University of Illinois at Urbana-Champaign, Illinois 61801, and Department of Chemistry, Northeastem University, Boston, Massachusetts 021 15 Received: July 25, 1994; In Final Form: October 11, 1994@

The rotational correlation time, ZR,is important to an analysis of the physical processes underlying proton relaxation enhancement by paramagnetic contrast agents. In this study, we report the successful applications of theoretical and experimental electron paramagnetic resonance (EPR) techniques to VO(DTPA) (DTPA = diethylenetriaminepentaacetic acid) in order to describe rotational dynamics of the paramagnetic complex, which is a model for similar sized paramagnetic contrast agents. EPR results are compared to nuclear magnetic relaxation dispersion (NMRD) measurements and are found to be in excellent agreement. Moreover, the distances of closest approach of protons to the central metal ion inferred from EPR, NMRD, and electron spin echo envelope modulation measurements all coincide. The data derived from EPR and NMRD for VO(DTPA) have been applied to model characteristics of Gd(DTF’A). The results show that “second-sphere” contributions to proton relaxation are not negligible. This work establishes a basis for the applications of EPR to study the rotational dynamics of virtually any type of paramagnetic contrast agent of interest.

1. Introduction

In general, MRI signal intensity is directly related to the longitudinal proton relaxation rate, 1/T1 (or relaxivity when normalized to concentration). Paramagnetic contrast agents can increase image contrast by increasing the relaxation rate of the protons contained in the tissue. Three processes can be envisioned as contributing to this relaxation enhancement. They are inner-sphere, second-sphere, and outer-sphere proton relaxation processes. Inner-sphere proton relaxation is due to the protons that are bound to the first coordination sphere of the contrast agent. Typically, inner-sphere proton relaxation enhancement has been described by the Solomon-Bloembergen equations:l s 2

where q is the number of coordinated protons, [MI is the concentration of the paramagnetic contrast agent, [MP] is the

* To whom correspondence should be addressed (E-mail: jwcj @rlb6000.scs.uiuc.edu). t Department of Chemistry, University of Illinois at Urbana-Champaign. Department of Veterinary Clinical Medicine. College of Medicine. Northeastern University. Abstract published in Advance ACS Absrracrs, November 15, 1994.

concentration of solvent protons (111 mom), y~ is the nuclear gyromagnetic ratio, po is the permeability of vacuum, p~ is the Bohr magneton, S is the electron spin, w s and OI are the corresponding electron and nuclear Larmor frequencies, TIMis the relaxation time of inner-sphere coordinated protons, g is the electronic g factor (assumed to be isotropic), r is the protonmetal-ion distance, and As is the nuclear-electron hyperfine coupling constant. The correlation times tc and re are defined as follows:

where ZR is the rotational correlation time for the entire agentproton complex, Z M is the residence lifetime of the bound protons, and rs is the electronic spin relaxation time. The Solomon-Bloembergen theory can also be applied to describe second-sphere proton relaxation, in which protons relax via hydrogen bonding to the contrast agent; however, only the dipolar term of eq 1 applies to second-sphere proton relaxation, as protons are not bound strongly enough to the metal ion to experience substantial contact interaction. Outer-sphere proton relaxation, or relaxation due to protons diffusing near the agent, may be rotationally andor translationally modulated. Outer-sphere relaxation modulated by rotational diffusion can be described by the following equation^:^

* *

@

0022-365419412098-13452$04.5010

0 1994 American Chemical Society

Rotational Dynamics of Paramagnetic Contrast Agents

=

tC

1

J. Phys. Chem., Vol. 98, No. 51, 1994 13453

(3)

+ w2z;

where

--C ‘

R ‘

(4) ‘S

n is the number of I spins in the solvation sphere of the S spins, d is the distance between the I and the S spins, and and [I] are the molar concentrations of the S and I spins, respectively. It is interesting that except for the exclusion of a proton resident lifetime (zM), eq 3 resembles closely the dipolar part of the Solomon-Bloembergen equations (eq 1). This is reasonable considering that in an outer-sphere model, the protons do not bind to the paramagnetic complex, and interact with the paramagnetic ion via a dipole-dipole mechanism. The boundaries of these spheres are not necessarily crisp and distinct; a clear understanding of the dimensions of the transition zone, where the second-sphere description under the SolomonBloembergen equations becomes the outer-sphere description under eq 3, is an important and interesting question for further study. The translationally modulated outer-sphere diffusion contribution to T I ,based upon a rigid-sphere m0de1,~-~ is

[a

j ( w ) = Re x

1 1

+ (iwz +

2/2,)’/2

+ l/,(iwz + 2/zs)1/2 + 4/9(i0z+ z/zs) + l/,(iwz + z = 32, = a2/D

I

2/2s)3‘2

(5)

where a is the distance of closest approach between the solvent protons and the paramagnetic complex, NA is Avogadro’s number, and D is the sum of the diffusion coefficients for the solvent protons and the agent. It should be mentioned that in the standard Bloch description of spin relaxation there actually are two electronic relaxation times, namely, the longitudinal (zs,) and the transverse ( t s z ) . However, in the discussion of paramagnetic contrast agents, they often are assumed to be equaL5s6 We shall also make this assumption in this work. Equations 1,4, and 5 show that several correlation times and distances are important to the proton relaxation enhancement: ZR, ZM, ZS, ZD, r, a, and d . A rational design of paramagnetic contrast agents ideally should optimize all the above parameters to achieve molecular structures which yield the best contrast. Nonetheless, to date, few studies have focused on achieving reliable and accurate determinations of these parameters for paramagnetic contrast agents. A fitting of nuclear magnetic resonance dispersion (NMRD) profiles could, in principle, yield these parameters, which represent the various physical properties. However, since the theories used to simulate the profiles, as exemplified by the above-mentioned equations, involve the simultaneous effects of many variables which affect the NMRD profiles in nonseparable ways, the solution derived by fitting NMRD simulation to experiment is not unique.7 Therefore, it is advantageous in simulating NMRD profiles that some, if not most, of the parameters be determined independently by other methods. Since the interactions represented by these parameters may not be

separated easily, it is important to develop methods that eliminate or minimize the role of the other parameters when making measurements on one of them. From a mathematical point of view, it is apparent from an examination of eqs 1 and 4 that the rotation of the complex plays an important role in determining the effectiveness of proton relaxation enhancement in the first-sphere, second-sphere, and rotationally modulated outer-sphere relaxation. Even if outer-sphere relaxation is dominated by translational diffusion, Bertini et al. have shown that in many systems, the translational correlation time is proportional to the rotational correlation time.8 In addition, it is possible for outer-sphere relaxation to be both rotationally and translationally modulated.6 From a physical point of view, the rotation of the paramagnetic complex is even more important in determining the overall relaxivity. A small-chelate paramagnetic contrast agent has a ZM approximately 1 ns to 1 A typical Gd(III) contrast agent has a zs around 1 ns. On the other hand, t~ is around 2 orders of magnitudes smaller ( ~ 0 . 0 1ns) at physiological temperature for small-chelate paramagnetic contrast agents such as Gd(DTPA) in water. Therefore, from eq 2, ZR would dominate tc until ZR is similar to ZM and/or ZS. Experiments have been performed whereby the paramagnetic contrast agent was attached to large macromolecules to slow the rotation of the complex. The results have in general been an increase in the relaxivity. Wiener et al.have shown that dendrimeric systems can further optimize this increase in ZR by minimizing internal motion., Moreover, it is also known that the electronic relaxation times and the rotational correlation times can be interdependent. [It is possible that in a macromolecular system where ZR ZS,eq 1 no longer holds since the Redfield limit is no longer met.] Therefore, ZR is extremely important in determining the proton relaxation enhancement not only in the rotationally modulated outer-sphere regime (and translationally modulated outer-sphere regime, as discussed above) but also in both inner-sphere and second-sphere relaxation enhancements. This study reports and details the successful application of EPR to determine the rotational correlation times of model paramagnetic contrast agents. We believe this approach can be used to investigate similar motional parameters in a wide range of contrast agent systems. 2. Methodology

It is not trivial to determine ZR since it is only indirectly coupled to most observable processes, NMRD. A simulation of the NMRD profiles can provide much information, but because of the large number of physical parameters involved, fitting the relaxivity data alone leads to multiple solutions. While 13CNMR coupled with nuclear Overhauser enhancement (NOE) has been used to estimate ZR,~Othis method has the major drawback that ZR is estimated as a function of other variables and thus does not satisfy the ideal requirement of isolating ZR from other variables. Fluorescence is widely used to investigate rotational dynamics, but very few potential contrast agents fluoresce; therefore, synthesis of analogues of the contrast agents incorporating suitable fluorophore labels would be necessary. However, in such labeling, one would risk changing the complex’s size and shape and hence alter the rotational dynamics of the contrast agent in which we are interested. On the other hand, the use of EPR to determine the rotational correlation time is more direct: for a given paramagnetic complex that has suitable Zeeman or non-Zeeman anisotropies, molecular rotation can be the principal source of modulation of the EPR line shape. EPR spectra often are extremely sensitive to rotational motion; thus, ZR may be determined by simulation of the spectral line

Chen et al.

13454 J. Phys. Chem., Vol. 98, No. 51, 1994 shape. Until now, however, motional studies of paramagnetic contrast agents by EPR have not been successful because the paramagnetic ion most generally used, complexed gadolinium (Gd3+),is virtually isotropic and thus does not exhibit rotationally modulated EPR spectra at conventional magnetic fields (0.33 T). However, we circumvented this problem by recognizing that rotational motion is predominantly a function of molecular size and shape,1° so that the motion of complexes that show motion-insensitive EPR can be modeled by EPR studies of similarly sized and shaped motion-sensitive paramagnetic complexes. Vanadyl (V02+), because of its very anisotropic g and A matrices, and nuclear spin Z = 7/2, exhibits strongly motionally modulated EPR spectra that can be accurately simulated. Therefore, in this study, we have applied variable-temperature EPR to study a model vanadyl complex-vanadyl diethylenetriamine pentaacetate (VO(DTPA))-that should be similar in size and shape to the clinically important paramagnetic contrast agent, Gd(DTPA). Through this model, we hope to demonstrate the methodology and study rotational dynamics of paramagnetic contrast agents. As a further check for this study, we have also performed variable-temperature NMRD experiments on the complex. The NMRD profiles have been simulated, with and without the EPR results, to demonstrate the accuracy of EPR in determining ZR and the usefulness of the EPR results to NMRD simulations.

3. Materials and Methods 3.1. Chemical Preparation All the chemicals of the highest grade were obtained from Aldrich. The stock vanadyl sulfate solutions were prepared from deionized water and purged with argon to prevent oxidation of the vanadyl ion (pH 2). Sample solutions were prepared by combining in a 1:1.2 ratio the stock vanadyl sulfate solution and the powdered DTPA. Sodium bicarbonate (5% solution) was used to raise the pH to physiological pH (=7.4). The final solution was diluted to approximately 3 mM with 50 mM HEPES buffer and again purged with argon. The concentrationsof the solutions were determined by plasma emission spectroscopy on a Perkin-Elmer Model P2000. 3.2. Spectroscopy. 3.2.I . WNis. UV/vis spectroscopy was performed on a Hewlett-Packard 8452 diode array spectrometer. The presence of a single W / v i s absorption peak at 654 nm for all of the sample solutions signified that chelation was complete. Small aliquots of the solutions were set aside and measured at intervals of 6 h for 1 day and then every day for a week to ascertain that chelation remained complete. We found that if the sample was kept under argon and refrigerated, the sample gave consistent UV/vis and EPR spectra even after several weeks have elapsed. 3.2.2. EPR. Variable-temperature EPR measurements were taken on a Varian X-band spectrometer (12 in. magnet) with a TE102 cavity encased in 1-in.-thick Styrofoam and fitted with a glass chimney to minimize condensation. The sample was held in a flat cell, and its temperature was regulated by flowing gaseous nitrogen precooled by liquid nitrogen through a Varian variable-temperature controller. We calibrated the temperature to obtain a correlation between the heater temperature and the actual temperature experienced by the sample by placing thermocouples both in the center and at the top of the flat cell compartment. Increasingly large temperature differences between the top and the center of the flat cell compartment were found as the system moves away from room temperature. Since we cannot place a thermocouple in the center of the flat cell compartment without affecting the spectra taken, we first measured the temperature at the top of the flat cell compartment

and then computed the actual temperature for the center of the flat cell compartment by using the calibration curve derived earlier. A standard field calibration utilizing a DTM-141 digital teslameter was also performed on the X-band spectrometer. 3.2.3. NMRD. Variable-temperature NMRD was performed on a Koenig-Brown IBM field cycling relaxometer (type blue) located in the Biomedical Magnetic Resonance Laboratory at the University of Illinois at Urbana-Champaign. Experiments were performed both on the sample to find the overall relaxation rate and on the blank saline solution to obtain the diamagnetic contribution to relaxation, since

- 1_ -- -1Tip

Tl

1 Tl,

where TI is the relaxation rate of the sample solution measured by NMRD, T1d is the diamagnetic contribution to the relaxation rate, and TlP is the paramagnetic contribution to the relaxation rate. 1/Tlp normalized to concentration (usually to 1 mM) is called relaxivity. 3.3. Computation. All computations were performed on an IBM RW6000 Model 320H, except for the powder pattern analysis, which was computed on a Gateway 2000 486DX2. All the software mentioned here may be obtained via anonymous ftp at the Illinois EPR Research Center. [To obtain the software at the Illinois EPR Research Center's ftp site use the following steps: 1. ftp rlb6000.scs.uiuc.edu. 2. At the login prompt type anonymous. 3. Enter your e-mail address as the password. 4. Type get README.lst to read what are on the site and where they are located. 5 . Change directory to the desired directory with the command cd directory-name. 6. Issue the command get filename to get the desired file. Please e-mail jwcj @rlb6000.scs.uiuc.edu if you have questions or problems.] 3.3.1. EPR. The powder pattern computation to derive A and g employed SIMPOW, a sibling program of QPOW."S'~ SIMPOW differs from QPOW in that it utilizes a second-order perturbative approach instead of matrix computation (see below). Motionally modulated spectra simulations used the EPRLF family of programs utilizing the stochastic Liouville equations that include nonsecular contributions in the spin Hamiltonian (see below). Automatic fitting programs incorporating the EPRLF simulation engine and based on Brent's method13 of parabolic interpolation was developed to visualize and compare the results of the simulation with those of the experiments. 3.3.2. NMRD. Multidimensional minimization programs based on the simplex method14for the Solomon-Bloembergen equations (eqs 1, 3, and 5 ) were written to simulate the NMRD profiles (see below).

4. Simulations 4.1. EPR. SIMPOW simulates the first derivative of a powder spectrum for a single unpaired electron based on the following spin-Hamiltonian:

where the terms on the right are the electronic Zeeman, metal hyperfine, nuclear Zeeman, metal quadrupole interactions, and the superhyperfine (ligand) interactions, respectively. For the application reported in this paper, superhyperfine interactions were not experimentally resolved. Therefore, the superhyperfine coupling matrices were set to zero, and the superhyperfine interactions were included in the line-broadening effect. The energy levels of the system are determined by solving the spin-

J. Phys. Chem., Vol. 98, No. 51, 1994 13455

Rotational Dynamics of Paramagnetic Contrast Agents Hamiltonian to a second-order level of perturbation. The resonance positions, transition probabilities, and line widths (Gaussian or Lorentzian) are interpolated at intermediate orientations to fill in a four-point Gauss-point integration grid. The simulated powder spectrum is then computed for points on a regular magnetic field grid. The EPRLF program used for the slow-motional line-shape calculations is based on the theoretical expressions for the stochastic Liouville matrix equation given by Meirovitch et al.l6 It is closely related to the EPRLL program published by Schneider and Freed,ls but more general in that it includes nonsecular g matrix and A matrix terms in the spin-Hamiltonian. Inclusion of nonsecular terms makes it possible to avoid the high-field approximation inherent in the EPRLL programs. This is an essential feature for calculating vanadyl ion spectra at X-band, given that the large hyperfine interaction in this ion is quite significant compared with the electronic Zeeman interaction at such frequencies. A second significant advantage of EPRLF is that it yields accurate rotational line widths over a fuller range of motions than EPRLL, specifically for very fast motions, when (zR)-~approaches the electronic Larmor frequency. EPRLF is also more general than the vanadyl ion calculations of Campbell and Freed,” which utilized a perturbative approach for including nonsecular terms and relied on a limited basis set that did not allow for deviations of the magnetic tensors from axial symmetry. The more general basis set used by EPRLF accommodated the slight deviation from axiality observed in the powder-pattern spectra of VO(DTPA) (see below), thus improving the accuracy with which the experimental spectra could be simulated. Finally, EPRLF can accommodate microscopic diffusion models other than the simple Brownian model used in the present work, which may be important for simulating vanadyl EPR spectra in other contexts. These models includels (i) jump and approximate free diffusion, which may be appropriate for smaller complexes in which the approximations underlying the Brownian diffusion model break down, (ii) a jumping motion between discrete sites related by an n-fold symmetry axis, which may apply to paramagnetic ion complexes in which a change in ligand bond distances can be represented by a simple rotation 2 d n , and (iii) fast internal rotations, which may be most appropriate for macromolecules to which a spin label such as a vanadyl ion is attached by a flexible linkage. The detailed theoretical formulas used in the EPRLF program for the additional terms not included in the published programs may be found in Appendices A and B of Meirovitch et a1.16 Moreover, for readers interested in pursuing work utilizing the computational tools developed for this study, the source and precompiled binaries for IBM RS/6000 AIX 3.2.5 of EPRLF is available at the Illinois EPR Research Center’s anonymous FTP site (rlb6000.scs.uiuc.edu). To carry out automated least-squares minimization of the simulations with respect to the experimental spectra, it was necessary to optimize the efficiency of the calculations by the basis-set pruning scheme of Vasavada et al.19 Briefly, the stochastic Liouville equation was constructed with a basis set known to be large enough to represent a given motional rate for the vanadyl ion, and the equation solved at each of a series of field points across the spectrum. At every point, the projection of each basis vector upon the solution vector was calculated, and its maximum projection (or “significance factor”) was stored. The basis set could then be pruned by defining a cutoff tolerance and retaining only those basis vectors with significance factors larger than the cutoff. The cutoff tolerance

TABLE 1: Best-Fit Powder Pattern Parameters for VO(DTPA) A,‘(MHa)

-186.1‘

A,“(MHz)

A,“(MHz)

-172.P

-508.2’

,g 1.980

g , 1.978

g , 1.944

a 1MHz = (gis,,)B/h= 2.75 G for VO(DPTA). The corresponding values of A under the definition in a are A, = -67.6 G, A, = -62.5 G, A, = -184.6 G.

of 0.015 that we found to be generally required for satisfactory representation of the slow-motional continuous wave (cw) vanadyl spectra is slightly smaller than the 0.03 recommended by Vasavada et al. for cw spectra. This difference may be due to the much larger hyperfine interaction in the vanadyl ion than in the nitroxides for which these workers performed their calculations. Nevertheless, the basis set pruning resulted in over an order-of-magnitude reduction in computation time. To obtain the rotational correlation times and carry out the residual line-width fitting, we fist fitted the rotational correlation times with the residual line width arbitrarily fixed at 1.0 G. After the rotational correlation time was obtained for each spectrum, ZR was then fixed while the fitting program varied the residual line width to obtain a”. This procedure was repeated to make sure the results obtained were the best-fit values. 4.2. NMRD. The application of the Solomon-Bloembergen equations (eq 1) to simulate NMRD profiles of aquo vanadyl ion has been studied by Bertini et aL20 for inner-sphere relaxation enhancement. However, in VO(DTPA), since vanadyl has at most six coordination sites, and one is already occupied by the axial oxygen, at most only five sites are available to coordinate with the octadentate DTPA. Therefore, VO(DTPA) is likely to have no inner-sphere water. The relaxivity observed is then due to either second-sphere water, outer-sphere water, or both. Several different models of relaxation enhancement were tested with our NMRD data. Among the models tried were second-sphere (eq l), rotationally modulated outer-sphere (eq 3), and translationally modulated outer sphere (eq 5). Among these models, only the second-sphere mechanism adequately fitted our data. Therefore, we adopted the second-spheredominated mechanism for further data analysis, which allowed us to simplify eq 1 by excluding the contact term. Only five parameters then need to be fitted by the simulation. They are ZR,ZM,ZS, r, and q. However, now q is the number of hydrogenbonded protons, ZM is the residence lifetime of the hydrogenbonded protons, and r is the distance between these protons and the paramagnetic ion. Note that the definitions of ZR and zs remain the same, regardless of whether the mechanism being considered is inner sphere, second sphere, or outer sphere. Although zs generally is observed to be field-dependent, vanadyl complexes seem to exhibit field-independent In our simulation, we shall make the assumption that electronic relaxation is modulated by rotation and is proportional to ZR.

5. Results and Discussion The rigid-limit powder pattern spectra taken at 173 K were used to first derive the hyperfine coupling constants A and g for VO(DTPA). The complex spectral features exhibited in the Z = ’/2 vanadyl ion allow the g matrix and the A matrix to be accurately determined. Deviations as small as f 1 . 5 MHz in the elements of A and f O . O O 1 in the elements of g produce noticeable differences between the simulated and the experimental powder pattern spectra. The resulting rigid-limit parameters are shown in Table l. They are very similar to those

13456 J. Phys. Chem., Vol. 98, No. 51, 1994

Chen et al. (d) 261 K

2000

2500

3000 3500 4000 Magnetic Field (Gauss)

4500

(b) 2 8 6 K

2000

2500

3000 3500 4000 Magnetic Field (Gauss)

(e) rigid limit

2000

2500

3000 3500 4000 Magnetic Field (Gauss)

4500

2000

2500

3000 3500 4000 Magnetic Field (Gauss)

4500

2000

2500

4500

I

3000 3500 4000 Magnetic Field (Gauss)

4500

Figure 1. Some representative VO(DTPA) EPR spectra and their best-fits: (a) nearly motionally narrowed spectrum: best-fit t~ = 5.95 x lo-” s, a” = 3.49 G , (b) characteristic spectrum showing the onset of the slow tumbling regime: t~ = 1.56 x s, a” = 0.51 G, (c) slow tumbling s, a” = 0.00 G, (d) spectrum where anisotropies spectrum; asymmetric broadening relative to the field center is quite evident: t~ = 2.90 x s, a” = 2.54 G, (e) the rigid-limit spectrum and its best-fit. in A and g are evident and becoming resolved; t~ = 3.82 x

published in earlier vanadyl studies.” Small deviation from axial symmetry was observed. The values obtained in Table 1 were used as fixed input parameters for the dynamic EPR simulations. The excellent agreement obtained between the simulated and the experimental spectra using these values (Figure 1) led us to conclude that the A matrix and the g matrix for VO(DTPA) are nearly independent of temperature, at least for the temperature range studied. A model of isotropic Brownian diffusion was used in the slow-motional spectral calculations. The rotational correlation time ZR was computed from the isotropic rotational diffusion rate constant, DR,derived from the least-squares spectral simulation, by the following relationship:21

D, = 1/67, Because of the high spectral complexity of vanadyl complexes, even at fast rotational rates, very high accuracy in TR values could be obtained; for example, a difference of only ~ t 2 % in t~ led to detectable differences in the simulated spectrum. Furthermore, there was a one-to-one relationship between TR and its corresponding spectra; that is, each spectrum could only

be simulated, within the error mentioned above, by one unique rotational correlation time. The experimental EPR line widths include several contributions besides those due to rotational modulation of the magnetic tensors. This “residual line width” arises from the inhomogeneous broadening due to unresolved hyperfine interactions of the vanadyl ion with nuclei on the ligands and to environmental variations, as well as from homogeneous, dynamic contributions due to spin-rotational coupling and Heisenberg spin exchange. Thus the line width may in general reflect both Lorentzian and Gaussian contributions to the residual broadening. As an approximation, we modeled the residual line widths by adding an additional Lorentzian line-broadening term, a” in the spectral fits, as has been done in previous w ~ r k . ’ ~ , Since ~* the simulations gave quite good fits to the experimental spectra, with R2 values typically exceeding 0.98, we judged the inclusion of Gaussian (Voigt) broadening to be unnecessary. The overall line shapes are also well-reproduced by the simulations, although in some cases the relative line intensities do not match perfectly. Such good overall agreement indicates that the model of isotropic motion used here for the slow-motional EPR simulations is quite reasonable for the VO(DTPA) complex. This is

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Rotational Dynamics of Paramagnetic Contrast Agents

TABLE 2: Best-Fit Rotational Correlations Times (ZR)and Residual Line Widths (a”)for VO@TPA) from EPR T (K) ZR (s) a” (G) R2 327 300 286 276 266 26 1 256

5.95 x 10-11 1.05 x 1.56 x 2.08 x 2.90 x 3.82 x 7.19 x 10-09

3.49 0.92 0.51

0.00 0.00 2.54 1.97

0.98 0.99 0.99 0.98 0.97 0.96 0.98

consistent with what is expected from the nearly spherical shape of this complex, especially when bound water molecules are included. More importantly, this result confirms the basic validity of the assumption of isotropic rotation for ZR used in the derivation of eqs 1 and 3 for VO(DTPA) and similarly shaped contrast-agent molecules. The very small differences in line intensity between simulated and experimental spectra in some cases may be caused by the difficulty in maintaining the baseline over large field measurements and at low temperatures, or they may result from small deviations from isotropic rotation of the VO(DTPA) complex. Table 2 lists the best-fit rotational correlation times and residual line widths obtained for VO(DTPA), and Figure 1 shows some representative VO(DTPA) EPR spectra together with their respective simulations. These spectra demonstrate that EPR is sensitive to rotational motion over a wide dynamic range. At or near the motionally narrowed region, the spectra are characterized by roughly equally spaced Lorentzian lines, as shown in Figure la. A typical ZR for such a spectrum is 110-11 s. This is the expected rotational correlation time estimated from the oszc % 1 NMRD dispersion for Gd(DTPA) or similar sized molecule at or above the physiological t e m ~ e r a t u r e . The ~ ~ simulation best fitted this spectrum at ZR = 5.95 x lo-” s. As the temperature was decreased, the spectrum broadened, and asymmetry in the line shape became apparent in the spectra, as shown in Figure lb,c. This is because as tumbling slows down, the motion becomes insufficient to average completely the asymmetric, anisotropic contributions to the line shape. The best-fit ZR’S in this region are 2.08 x and 2.90 x s, respectively. This is the onset of the slow tumbling region, which is characterized by asymmetric line broadening at both ends of the spectrum and a significant increase in the relative intensity of the central line of the spectrum. At around ZR % s, as exemplified by Figure Id (ZR = 3.82 x s), the spectrum becomes more complex, and the anisotropy in g and A become apparent. The central line is now the dominant feature in the spectrum. Figure l e shows the rigid-limit spectrum and its best fit by SIMPOW. The residual line widths obtained from the spectral fits and given in Table 2 follow a trend similar to that observed by Campbell and Freed for vanadyl bis(acety1acetone)propylenediimine (VO(acac2(pn))).l7 A significant residual broadening is observed at the highest temperatures (in the motionally averaged regime), which decreases as the temperature is dropped and approaches a “constant” value in the slow-tumbling region. In fact, no residual broadening was needed at all in our simulations at the two lowest temperatures in the slow-tumbling region. The fits in this temperature range were relatively insensitive to the value of a”,which probably results from the predominance of the rotational line-width contributions over the residual line width at longer ZR values. In approaching the incipient rigid limit, the residual line width found from our fitting procedures increases. Again, a corresponding increase has been observed in the study done by Campbell and Freed17 for VO(acacn(pn)) in toluene, in which a” was observed to increase from 1.7 G at ZR = 2.25 x

P

I

n v) W

t-“

5’

10-3

3

2

T/T

4

5

6

7

8

9

(CPS/K)

.Figure 2. r~ vs q/T for VO(DTPA). The boxed graph represents the entire range of ~ R ’ Sstudied. Note that once the solution reaches its freezing point, there is a dramatic increase in t ~ .

s to 6 G at ZR = 5.0 x lo-* s. In our study we found that the residual line width increases from 0 to ~2 G at about ZR a s, which is intermediate to the two lowest ZR values reported by Campbell and Freed but consistent with the overall trend in residual line width observed by these workers. This increased line width near the rigid limit most likely reflects site inhomogeneities introduced into the sample by the freezing process. The high residual line width observed above physiological temperatures most likely arises from Heisenberg spin exchange between vanadyl ions, considering the 3 mM concentration used in the experiments. This contribution diminishes as the mutual diffusion rate for vanadyl slows down at lower temperatures. Throughout the slow-tumbling region there was no evidence for the unusually large spin-rotational contributions reported by Wilson and Kivelson,22 which would indicate significant deviations from Brownian diffusional behavior.24 We conclude that the small residual linewidth in the incipient slow-tumbling region arises from a negligible amount of inhomogeneous broadening. In addition, the absence of any significant nonBrownian behavior in the VO(DTPA) complex offers further support for the validity of the Brownian diffusional model used to derive eqs 1-5. It should be noted that these EPR experiments were performed at ~9 GHz (X-band), for which 0 s - l % 1.76 x s. This would be the fast tumbling limit to the sensitivity of our experiment. To improve the sensitivity, higher frequency instruments such as 35 GHz (Q-band) and 94 GHz (W-band) EPR spectrometers can be employed. Our simulation software will readily simulate spectra obtained at these higher fields. In fact, the slow-motional line-shape calculations are greatly simplified at the higher frequencies, since it is possible to take advantage of the high-field approximation and utilize the more efficient EPRLL programs. Nonetheless, because it is often necessary to complex the paramagnetic species with chelating agents to reduce toxicity, paramagnetic contrast agents, under clinical conditions, do not exhibit rotational correlation times faster than the X-band limit for these vanadyl complexes. Moreover, since a slower tumbling rate is associated with an increase in relaxivity, we are more often interested in obtaining ZR slower than the upper X-band limit. The situation would be different for contrast agent models labeled with paramagnetic centers, like nitroxides, that are less anisotropic than vanadyl complexes. Figure 2 illustrates how well the rotational motion in VO(DTPA) obeys the Stokes-Einstein equation:

13458 J. Phys. Chem., Vol. 98, No. 51, 1994

Chen et al. 0.5 1

(9) where 17, the viscosity of the solution, is taken to be that of water at the respective temperature^?^ r is the hydrodynamic radius, k~ is the Boltzmann constant, and T is the temperature of the solution. The linearity of the plot supports the contention that eq 9 is a valid description of these complexes. At -265 K, as shown in the boxed graph, the solution freezes and there is a dramatic increase in the rotational correlation times. These points were not included in the analysis since the lower temperature data points represent a different environment (near solid phase). However, they do demonstrate that EPR is sensitive to this change in environment. Therefore, EPR investigations would be useful in measuring rotational correlation times of other paramagnetic contrast agents such as those linked to macromolecules. The hydrodynamic radius (r) derived from a linear regression of Figure 2 is 4.71 A. This is a reasonable value. Assuming that one layer of water is hydrogen bonded to the complex and estimating that this layer is -0.9 8, thick (the water 0 - H bond we obtained a value of %3.8 8, for the length is 0.958 distance of closest approach between the water protons and the paramagnetic ion. This is extremely close to the value of 3.9 8, obtained for Gd(DTPA) by ESEEM.26 This value further is verified in the NMRD simulations, presented in Table 3, where the best-fit distance between the hydrogen-bonded protons and the paramagnetic ion is very close to 3.8 A. The good agreement between the VO(DTPA) hydrogen-bonded protonmetal ion distance and that measured in Gd(DTPA) strengthens the initial assumption that the sizes of VO(DTPA) and Gd(DTPA) are similar. Consequently, the rotational correlation times obtained for VO(DTPA) can be applied to describe Gd(DTPA). Similarly, other vanadyl complexes can be prepared to probe the rotational motion of their gadolinium analogues. Table 3 lists the best-fit parameters obtained for the VO(DTPA) NMRD profiles under the Solomon-Bloembergen equations and Figure 3 shows the corresponding simulations. The simulation matches the experimental curves quite well. In the process of obtaining the best-fit simulations, several minima were encountered. However, from the EPR studies we have already obtained two parameters, namely, ZR and r. Therefore, we can choose the solution sets that contain ZR and r values close to what we have obtainedfrom EPR. This proved to be a very reliable method of obtaining consistent solutions: the simulation then always converged to the same set of solutions for a given profile. Moreover, we did not fix the values of ZR and I in simulating the NMRD profiles; we allowed the simulation to fine tune ZR and r values for each profile to make sure that there are no other solution sets with similar ZR and r. Two things are noteworthy in examining Table 3. First, the rotational correlation times derived from NMRD agree extremely well with the EPR results. Second, as alluded to before, the distance between the second-sphere protons and the aramagnetic ion obtained from NMRD is approximately 3.8 l a n d confirms the result from ESEEM26 and EPR. The simulation yielded proton residence lifetimes (ZM) that are longer than what one might expect. It is possible that this is a manifestation of the limitation of the Solomon-Bloembergen (eq 1) in describing this system. However, Bertini et al. have found long ZM values (-10 ps) for the equatorial proton exchange (inner-sphere) for the vanadyl aquo ion.*O Altematively, DTPA, with its many negative charges, potentially could bind protons for a very long time, causing the slow exchange. That the ZM'S fitted are relatively constant over the temperature range studied suggests that for a "second-sphere" mechanism,

278 K

O.b.bl,

'

"""'

0.1

'

" '

"""'

1

'

'

"""'

10

'

Proton Lormor Frequency (MHz)

Figure 3. NIvlRD profiles and best-fit curves for VO(DTPA) for the four temperatures studied. As temperature increases from 278 to 293 K, the relaxivity decreases by almost 30%.

TABLE 3: Best-Fit Parameters for VO(DTPA) NMRD Profiles Using Eq 1 temp (K) 278 284 289 293 TR NMRD (ns) 0.183 0.152 0.131 0.119 ZR EPR

(ns)

% error from EPR results ZM

rrs( g

R2

@s)

!r) 1

0.183

0.00 682 15.5 3.79 84.6 0.9997

0.151 0.66 711 13.3 3.83 83.0 0.9999

0.131 0.00 745 12.5 3.83 78.8 0.9998

0.118 0.85 719 11.7 3.83 75.8 0.9998

the rate of proton exchange may not decrease with temperature as is expected for an "inner-sphere'' process. However, we cannot exclude the possibility that this is an artifact from the small temperature range studied. Another possibility is that ZM may not be an independent process and may be coupled to either rotation, electronic relaxation, or both. Electronic relaxation times derived for VO(DTPA) are relatively short. Nonetheless, Bertini et al. have obtained similar electronic relaxation times for vanadyl aquo ion.20 Since electronic relaxation in vanadyl is modulated by hyperfine interactions (A anisotropy) between the vanadyl electron and the neighboring nuclei,*' the presence of a large number of protons as obtained from the fitting may aid in expediting electronic relaxation. Moreover, based on the structure of the complex, the large number of "second-sphere" protons is expected. An order-of-magnitude surface area calculation reveals that more than 200 water molecules can fit on the surface of VO(DTPA). There is a small decrease in the number of "second-sphere" protons as the temperature is increased, perhaps indicating that as the complex rotates faster, fewer protons are able to hydrogen-bond successfully to the paramagnetic complex. We attempted to improve the simulations of the NMRD profiles by including a field-dependent zs for vanadyl.20 However, we found the fitting to be poor. Therefore, we conclude from this that the best assumption is that zs for VO(DTPA) is field-independent, as was shown later in ref 17. We also tried eqs 3 and 5 to fit the NMRD profiles but have not found good agreement between the simulations and the experiments. The parameters obtained for VO(DTPA) should be comparable to those for Gd(DTPA) as well. As noted before, the molecular sizes of the two complexes, as indicated by their similar r, are nearly identical. With the same chelating agent, the shapes of these two complexes should be similar. Therefore, the rotational correlation times can be used to describe Gd-

J. Phys. Chem., Vol. 98, No. 51, 1994 13459

Rotational Dynamics of Paramagnetic Contrast Agents (DTPA). Assuming that Gd(DTPA)’s other parameters are identical to those of the vanadyl NMRD solutions (except for metal dependent constants such as y ~ S, , and OI),we have calculated, utilizing the second-sphere model, relaxivity values of ~ 0 . 8 6mM-’ s-l for the Gd complex at low fields (0.02 to e 5 MHz) and ~ 0 . 7 mM-’ 7 s-l at high fields ( > 5 MHz). This can account for more than 10% of the relaxivity Gd(DTPA) at low fields and more than 15% at high fields (based on the relaxivity data for Gd(DTPA) contained in ref 19). If, however, we take into account that electronic relaxation in Gd3+ complexes is modulated by zero-field splitting:’ which may not be as strongly influenced by the large number of protons nearby, the relaxivity increases to greater than 0.94 mM-’ s-l (using a zs = 1 ns). Therefore, this seems to indicate that the “second-sphere’’relaxation process cannot be ignored in analyzing Gd(DTPA) and other similar complexes.

6. Conclusions In this work we have established and confirmed that the rotational dynamics data obtained from EPR studies on vanadyl complexes can be used to describe the rotational dynamics of similar gadolinium complexes. This lays the groundwork for many future studies to measure the rotational correlation times of not only small chelated paramagnetic complexes but also paramagnetic complexes bound to large macromolecules. Rotational dynamics of paramagnetic contrast agents bound to macromolecules are of particular clinical interest because the contrast agents may bind to proteins and other macromolecules once injected into the blood or the target tissue, either advantageously or by design. NMRD results on VO(DTPA) provide much information and have been used to describe a “second-sphere’’relaxation process in Gd(DTPA). The results indicate that “second-sphere’’ contributions to the relaxivity are not insignificant. More work is in progress to elucidate the relaxation process in paramagnetic contrast agents. Acknowledgment. We thank Professor Paul Lauterbur for the use of his relaxometer and Dr. Erik Wiener and Dr. Alan Marumoto for assistance in its use. We are grateful to Dr. Mark Nilges for his SIMPOW program and discussions concerning

SIMPOW. We also thank Dr. David Schneider and Dr. Alex Smimov for useful discussions. Most other facilities were provided by the Illinois EPR Research Center, an NIH Biomedical Technology Research Resource (P41-RRO1811). Partial support for this work was provided by the NIH (GM-42208).

References and Notes Solomon, I. Phys. Rev. 1955, 99, 559. Bloembergen, N. J. J. Chem. Phys. 1957, 27, 572. Polnaszek, C. F.; Bryant, R. G. J . Chem. Phys. 1984, 81, 4038. Hwang, L.-P.; Freed, J. H. J. Chem. Phys. 1975, 63, 4017. (5) Bennett, H. F.; Brown, R. D., m, Koenig, S. H.; Swartz, H. M. Magn. Reson. Med. 1987, 4, 93. (6) Lauffer, R. B. Chem. Rev. 1987, 87, 901. (7) Luchinat, C. Magn. Reson. Chem. 1993, 31, S145. (8) Bertini, I.; Briganti, F.; Xia, Z.; Luchinat, C. J . Magn. Reson., Ser. A 1993, ZOZ, 198. (9) Wiener, E. C.; Auteri, F. P.; Belford, R. L.; Clarkson, R. B.; Lauterbur, P. C. Abstract to the Twelfth Annual Scientific Meeting of the Society of Magnetic Resonance in Medicine, 1993, 241. (10) Aime, S.; Botta, M.; Terreno, E.; Lucio Anelli, P.; Uggeri, F. Magn. Reson. Med. 1993, 30, 583. (11) Nilges, M. J. Ph.D. Thesis, University of Illinois, 1979. (12) Mabbs, F. E.; Collison, D. Electron Paramagnetic Resonance of d Transition Metal Compounds; Elsevier: Amsterdam, 1992; Chapter 7. (13) Brent, R. P. Algorithms for Minimization without Derivatives; Prentice-Hall: Englewood Cliffs, NJ, 1973; Chapter 5. (14) Nelder, J. A.; Mead, R. Comput. J. 1965, 7, 308. (15) Schneider, D. J.; Freed, J. H. A User’s Guide to Slow-Motional ESR Lineshape Calculations; Biological Magnetic Resonance; Vol. 8; Berliner, L. J., Reuben, J., Eds.; Academic Press: New York, 1989. (16) Meirovitch, E.; Igner, E.; Igner, D.; Moro, G.; Freed, J. H. J . Chem. Phys. 1982, 77, 3915. (17) Campbell, R. F.; Freed, J. H. J . Phys. Chem. 1980, 84, 2666. (18) Freed, J. H. Theory of Slow-MotionalESR Spectra for Nitroxides; Spin Labeling: Theory and Applications; Berliner, L. J., Ed.; Vol. I, Academic Press: New York, 1976; Vol. I. (19) Vasavada, K. V.; Schneider, D. J.; Freed, J. H. J . Chem. Phys. 1987, 86, 647. (20) Bertini, I.; Xia, Z.; Luchinat, C. J . Magn. Reson. 1992, 99, 235. (21) Goldman, S. A.; Bruno, G. V.; Polnaszek, C. F.; Freed, J. H. J . Chem. Phys. 1972, 56, 716. (22) Wilson, L.; Kivelson, D. J . Chem. Phys. 1966, 44, 154. (23) Koenig, S. H. Magn. Reson. Med. 1991, 22, 183. (24) Hoel, D.; Kivelson, D. J . Chem. Phys. 1975, 62, 4565. (25) CRC Handbook of Chemistry and Physics, 67th ed.; Weast, R. C., Astle, M. I., Beyer, W. H., Eds.; CRC Press, Inc.: Boca Raton, FL, 1986. (26) Clarkson, R. B.; Hwang, J.-H.; Belford, R. I. Magn. Reson. Med. 1993, 29, 521. (27) Luchinat, C.; Xia, 2. Coord. Chem. Rev. 1992, 120, 281. (1) (2) (3) (4)