Estimating the Number of Bound Waters in Gd(III) - American

q, have been applied to a test set of seven Gd(aminocarboxylate) complexes. ... complexed Gd ion (Castonguay, L. A., Treasurywala, A. M., Caulfield, T...
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Bioconjugate Chem. 2004, 15, 1496−1502

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Estimating the Number of Bound Waters in Gd(III) Complexes Revisited. Improved Methods for the Prediction of q-Values Benjamin P. Hay,*,† Eric J. Werner,§ and Kenneth N. Raymond§ Chemical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, and Department of Chemistry, University of California, Berkeley, California 94720-1460. Received July 9, 2004; Revised Manuscript Received September 27, 2004

Two literature computational methods for the prediction of the number of inner-sphere aqua ligands, q, have been applied to a test set of seven Gd(aminocarboxylate) complexes. The first method is based on the hypothesis that q should be proportional to the solvent-accessible surface area of the ligandcomplexed Gd ion (Castonguay, L. A., Treasurywala, A. M., Caulfield, T. J., Jaeger, E. P., and Kellar, K. E. (1999) Prediction of q-Values and Conformations of Gadolinium Chelates for Magnetic Resonance Imaging. Bioconjugate Chem. 10, 958). The second method is based on the hypothesis that q-values can be deduced by examining series of steric energy versus ionic radii plots as a function of coordination number (Reichert, D. E., Hancock, R. D., and Welch, M. J. (1996) Molecular Mechanics Investigation of Gadolinium(III) Complexes. Inorg. Chem. 35, 7013). This study identifies deficiencies in these methods and, with respect to the first method, describes some apparent errors. Although neither method was reliable at predicting q, two alternate approaches based on either molecular mechanics strain thresholds or exposed Gd surface area thresholds are shown to predict observed q-values for all Gd aminocarboxylate complexes in the test set.

INTRODUCTION

Magnetic resonance imaging (MRI) has become an important tool in modern medicine, providing high-quality three-dimensional images without the use of harmful ionizing radiation (1). Signal intensity in MRI stems mainly from the relaxation rate of in vivo water protons and is enhanced by the administration of a contrast agent prior to the scan. Such agents include a paramagnetic metal ion that decreases the relaxation times of nearby water protons. Contrast media often employ gadolinium(III) due to its high magnetic moment and slow electronic relaxation rate. As free Gd(III) is toxic (2), the design of ligands that form stable Gd(III) complexes for MRI application remains a significant area of research (2-4). The efficacy of Gd-based contrast agents is determined by the extent to which the relaxation rate of water protons is increased, in other words, relaxivity. Agent design focuses mainly on attaining higher inner-sphere, longitudinal relaxivity, r1, from protons of water molecules directly coordinated to the metal. Theory reveals the need to maximize q, the number of inner-sphere water molecules, to obtain optimal relaxivity (2, 3). Simply decreasing the number of binding sites in the ligand will lead to higher q-values, but may weaken the Gd-ligand binding and possibly release free Gd(III) in vivo. Therefore, one design goal for MRI contrast agents is to increase the q-value without significantly decreasing the binding affinity of the ligand (2-4). The ability to predict q prior to synthesis and testing would facilitate the design of improved contrast agents. Molecular dynamics simulations of Gd-ligand complexes in aqueous solution have been shown to predict correctly * To whom correspondence should be addressed. E-mail: [email protected]. † Pacific Northwest National Laboratory. § University of California, Berkeley.

the number of bound waters in several cases (5). However, such simulations require a significant amount of computational resources and are not suitable for the evaluation of large numbers of candidate structures. This situation has prompted the development of simpler methods for estimating q from static structures that have been optimized with molecular mechanics models. One approach is based on the hypothesis that q should be proportional to the solvent-accessible surface area of the ligand-complexed Gd ion (6). Another approach is based on the hypothesis that q-values can be deduced by examining a series of steric energy versus ionic radii plots as a function of coordination number (7). Our interest in these methods originated from a desire to apply them to a new family of potential MRI agents that are based on catecholate and hydroxypyridinonate donor groups (8). As the first step toward this goal, we chose to test the predictive capability of these methods on known compounds. Since the reported methods were tested primarily on aminocarboxylates, we selected a set of aminocarboxylate ligands for this verification. The test set, shown in Figure 1, was chosen for two reasons. First, q-values in aqueous solution, which span a range of 0 to 3, have been determined for these structures either via experimental measurement with the similar sized Eu(III) ion (2) and/or by MD simulation with the Gd(III) ion (5). Second, with the exception of NOTA, crystal structure data are available for Gd complexes with these ligands in which bound water is the only other inner-sphere ligand (9, 10). It is interesting to note that, in all cases where comparison is possible, the q-values in aqueous solution are in agreement with the number of bound waters observed in the crystal structures. After extending the MM3 model to treat Gd(III) complexes with aminocarboxylate and aqua ligands, we evaluated the ability of the “Connolly surface area” method (6) and the “coordination scan” method (7) to

10.1021/bc0498370 CCC: $27.50 © 2004 American Chemical Society Published on Web 10/26/2004

Technical Notes

Bioconjugate Chem., Vol. 15, No. 6, 2004 1497

Figure 1. Test set of aminocarboxylate ligands.

predict q-values for the ligand test set (Figure 1). Neither approach was entirely successful. The “Connolly surface area” method, which we find to be misnamed, fails to predict q-values for two out of the seven cases. The “coordination scan” method systematically underestimates q-values for all cases. Although the reported methods fail, the evaluation of optimized geometries for Gd(ligand)(O)n complexes, where n ) 0 to q + 1, yields alternative approaches that allow q-value predictions to be made for all seven cases using either Gd surface areas or strain energies. COMPUTATIONAL DETAILS

Force Field Model. Molecular mechanics calculations were carried out using the MM3 program (11), which has been modified to support POS metal atom types (12). In the POS approach (13), all “bound” ligand atoms are formally connected to the metal ion requiring the definition of M-L stretch, M-L-X bend, and M-L-X-X torsion potentials (M ) metal, L ) donor atom, X ) any other atom). All L-M-L angles are omitted, and van der Waals interactions between the L groups attached to the metal are added. In a recent study of steric interactions in U(IV) complexes, we have shown that the aqua ligand can be modeled as a neutrally charged oxygen atom (14), and the same approximation was used in this study. Prior parameter sets for Gd(III) complexes with aminocarboxylate and aqua ligands have been developed for POS force fields and shown to reproduce the geometries of these complexes with a fair degree of accuracy (7, 15, 16). Using these prior parametrizations as a starting point, we optimized geometries for Gd(EDTA)(O)3, Gd(DO3A)(O)2, Gd(DOTA)(O), Gd(DTPA)(O), Gd(THPA), and Gd(TTHA) complexes starting from their X-ray structure coordinates (10). The parameter set was then adjusted to minimize the sum of the rmsd values for superposition of calculated and experimental structures. The final parameter set and input files for all complexes are available as Supporting Information. Surface Area Calculations. Connolly surface areas and exposed van der Waals (VDW) surface areas for Gd were calculated with GEPOL (17). Tripose VDW radii used for the organic atoms were as follows: H, 1.500 Å; C, 1.700 Å; N, 1.555 Å; O, 1.520 Å (18). VDW radii for Gd were assigned based on the 53 Å2 surface area reported for the bare Gd ion (6). For the Connolly surface area calculations with a default probe radius of 1.40 Å, this surface area is achieved with a Gd radius of 0.65 Å. For exposed VDW surface area calculations this surface area is achieved with a Gd radius of 2.05 Å.

Calibration curves to establish the relationship between Gd surface area and q-value were prepared using the Gd(OH2)9 X-ray structure (19) with strict adherence to the published method (6). Gd surface areas were calculated for the structures obtained after removal of 0 to 9 water molecules from this crystal structure without any optimization. When there was more than one way to remove the water, all ways were examined subject to the following restriction. For n ) 2 to 8, only sets of contiguous waters were removed. A plot of surface area versus q-value was generated from the results. A second calibration curve was prepared for n ) 0 to 9 by plotting the Gd surface areas obtained from the model complex Gd(O)n where the complex was optimized with the MM3 model after the addition of each oxygen atom. Exposed VDW surface areas for the metal ion in Gd(ligand) complexes were obtained from MM3 optimized geometries. Initial geometries for these optimizations were taken from X-ray coordinates (10). For each complex investigated, the number of added oxygen atoms was varied from 0 to q+1. In cases where there was more than one possible placement for the oxygen atoms, all placements were tried and the lowest energy geometry was retained. Coordination Scan Calculations. Initial geometries for Gd(ligand)(O)n complexes were prepared as described above for n ) 0 to q. The size of the metal was varied by systematically altering the M-N and M-O equilibrium bond length parameters in the following manner: M-N bond length ) ionic radius + 1.7 Å; M-O bond length ) ionic radius + 1.4 Å. Scans were performed by varying the ionic radius from 0.5 to 1.5 Å in 0.1 Å intervals with the stretching force constant kept at a constant value of 0.695 mdyn/Å (equivalent to the 100 kcal/mol‚Å2 force constants used in the prior study) (7). Plots of steric energy versus metal radius were then generated for each coordination number and superimposed on the same graph. The results were interpreted with the following ionic radii for Gd(III): 0.94 Å for six-coordinate, 1.00 Å for seven-coordinate, 1.05 Å for eight-coordinate, and 1.11 Å for nine-coordinate environments (20). Strain Threshold Calculations. Initial geometries for each Gd(ligand)(O)n complex were prepared as described above for n ) 0 to q+1. After geometry optimization, the strain energy associated with adding the ith oxygen atom to the inner-sphere was taken as the difference Ui - Ui-1, where Ui is the steric energy of the complex with the ith oxygen atom present and Ui-1 is the steric energy of the complex before the ith oxygen atom was added.

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Technical Notes

Figure 3. Relationship between various Gd surface areas and q, where q ) 9 - number of bound aqua ligands. Literature values were taken from Figure 1 in ref 6.

Figure 2. Superposition of calculated and X-ray geometries. The rmsd value for each structure is given in parentheses. RESULTS AND DISCUSSION

Force Field Model Validation. Application of q prediction methods requires a molecular model to compute geometries for the Gd(ligand) complexes. The MM3 force field was extended to treat Gd(III) complexes with aminocarboxylate and aqua ligands. A model capable of reproducing the metal complex geometries observed in the solid state was obtained after adjusting parameters taken from prior POS force field models (7, 15, 16) to yield the best overall fit to crystal structure data (10). The rootmean-squared deviation (rmsd) between the calculated and experimental atom positions for all non-hydrogen atoms provides a measure of the accuracy of the model. In this instance the superposition of calculated and experimental structures, shown in Figure 2, yields an average rmsd of 0.156 Å. This level of accuracy is as least as good or better than that of the models used in prior q predictions (6, 7). “Connolly Surface Area” Method. A Connolly surface, also known as a solvent-accessible surface, is the surface traced out by the center of a test probe as it is rolled over a molecule (21). The Connolly surface for a single atom in a molecule can be computed as the surface traced out by the test probe center while the probe remains in direct contact with the atom. It was reported that the Connolly surface area for the Gd(III) ion in a Gd(ligand) complex can be used to predict the q-value for that complex (6). The stated method involves (1) optimization of a geometry for the Gd(ligand) complex, (2) calculation of the Connolly surface area for the Gd(III) ion, and (3) comparison of this surface area with a calibration curve relating surface area to the number of bound water molecules. The calibration curve was

purportedly generated by rolling a test probe of radius 1.4 Å over Gd(OH2)n structures, where n ) 0 to 9, to yield a linear correlation running from ∼53 Å2 for the bare Gd(III) ion to 0 Å2 for the nonaaqua ion. The reported relationship is depicted in Figure 3. Error bars on the points reflect the degree of variation resulting from removal of different sets of contiguous water molecules. We attempted to reproduce the calibration curve using atomic coordinates from the same Gd(OH2)9 X-ray structure used in the prior study. Default Sybyl force field VDW radii were used for the oxygen and hydrogen atoms. To calculate a Connolly surface area of ∼53 Å2 for the bare Gd(III) using a test probe radius of 1.40 Å, it is a mathematical requirement that the Gd(III) radius be set to a value near 0.65 Å. A plot of the Connolly surface area for Gd(III) versus the number of bound water molecules is also shown in Figure 3. Comparison of the Connolly surface areas to the surface areas reported in the prior study reveals a large difference in behavior, establishing that the reported values were not obtained by the Connolly method. Further calculations showed that computing a different geometric property, the exposed VDW surface area for the Gd(III) ion could largely reproduce the reported surface areas. This surface corresponds to the surface of the metal ion that would be visible in a space-filling model of the complex. Our calibration curve was not linear, however, showing a slight curvature at the higher coordination numbers (see Figure 3). Even with nine bound water molecules, 3.5 Å2 or 6.6% of the metal ion surface remains exposed. Another difference was a significantly smaller extent of area fluctuation as a function of the choice of contiguous water molecules removed. Where the literature calibration curve suggests fluctuations as large as (1.5 Å2 about the mean, our range of area values was less than (1.0 Å2 at any given coordination number. A second calibration curve was generated by computing the exposed VDW surface area for Gd(III) in a series of MM3 optimized model complexes, Gd(O)n, where n ) 0 to 9. Comparison with the average surface areas obtained by removing sets of contiguous water molecules from the Gd(OH2)n X-ray structure revealed that the Gd(III) surface areas differed by less than 1.0 Å2 at all coordination numbers. Thus, an exposed VDW surface area versus q plot essentially identical to that shown in Figure 3 is obtained by using (1) oxygen atoms to model aqua ligands

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Technical Notes

Figure 4. Interpolation of q-values for Gd(ligand) complexes from a plot of exposed VDW surface versus q generated from Gd(O)n complexes. Table 1. Exposed Gd VDW Surface Areas in Gd(ligand) Complexes and Predicted q-Values Interpolated from the Calibration Curve (Figure 4) ligand

surface area, Å2

q-value (calcd)

q-value (obsd)

EDTA NOTA DO3A DTPA DOTA TTPA TTHA

18.2 14.2 9.3 8.2 7.1 3.5 3.2

3.26 2.52 1.56 1.33 1.06 -0.26 -0.41

3 3 2 1 1 0 0

and (2) a single optimized geometry to calculate the surface area at each coordination number. This second calibration curve was used to predict q-values based on the exposed Gd VDW surface areas in MM3 optimized Gd(ligand) complexes (see Figure 4). The surface areas and predicted q-values are given in Table 1. The method successfully predicts q-values for five of the test cases, but leads to ambiguous predictions for DO3A, which lies midway between q ) 1 and 2, and NOTA, which lies midway between q ) 2 and 3. Thus, while there exists a definite trend between the exposed surface area of the metal ion in a nonhydrated Gd(ligand) complex and the number of water molecules that will bind, the method fails as an accurate predictor of q-value in two out of seven cases. There is an issue with using the exposed VDW surface areas obtained from Gd(ligand) structures that have been optimized in the absence of any bound water. Metalligand distances generally increase with increasing coordination number. Thus, the inner sphere will swell in size as more oxygen atoms are added. As the bound atoms move outward, more metal ion surface will be exposed. Therefore, the surface areas calculated for Gd(ligand) complexes will at best represent a lower limit to the actual area that is allowed by the ligand under consideration. This effect is observed by comparing the Gd surface area in the optimized Gd(ligand) geometry to that in an nonoptimized Gd(ligand) geometry created by removing the water molecules from the X-ray structure. For example, Gd(EDTA) exhibits18.2 Å2 in the optimized geometry versus 20.5 Å2 in the X-ray geometry and Gd(DTPA) exhibits 8.2 Å2 in the optimized geometry versus 10.1 Å2 in the X-ray geometry. “Coordination Scan” Method. This method involves calculation of the steric energy of the metal complex as

Figure 5. Coordination scan plots for EDTA (top), DO3A (middle), and DTPA (bottom).

a function of both metal ion size and coordination number (7, 22). These plots are superimposed to yield a family of curves. The curves exhibit intersection points that define zones of preferred coordination number as a function of metal ion size. By comparing the ionic radii of a metal ion in different coordination states to this family of curves it is possible to determine which coordination number is sterically favored for that metal ion. Using the extended MM3 model, coordination scans were performed on EDTA, NOTA, DO3A, DTPA, and DOTA. As illustrated by the examples shown in Figure 5, a series of intersecting curves are obtained on superposition of the scans. The EDTA plot shows that a sixcoordinate environment is preferred for metals with ionic radii below 0.85 Å, a seven-coordinate environment is preferred for ionic radii between 0.85 and 1.11 Å, an eight-coordinate environment is preferred for ionic radii between 1.11 and 1.28 Å, and a nine-coordinate environment is preferred for radii above 1.28 Å. Comparison with the ionic radii for Gd in different coordination states (0.94 Å, CN ) 6; 1.00 Å, CN ) 7; 1.05 Å, CN ) 8; 1.11 Å CN ) 9) predicts that Gd(EDTA) complex has a steric preference for a seven coordinate environment, thereby

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predicting q ) 1. Performing this analysis for the other ligands also predicts q-values that are too low: NOTA, q ) 1; D03A, q ) 0; DOTA, q ) 0; DTPA, q ) 0. These results are in disagreement with the prior application of this method (7) in which the correct q-values were obtained for these same ligands using a modified Tripose force field model, TAFF (18). We suspect the discrepancy between the results arises from differences in the TAFF and MM3 force fields. With the POS metal ion treatment used in both studies, the shape of the steric energy versus metal ionic radius curves will depend strongly on the VDW radii assigned to atoms attached directly to the metal ion. The VDW radii used in the TAFF model (nitrogen 1.555 Å, oxygen 1.520 Å) are significantly smaller than those used in MM3 model (nitrogen radius 1.93 Å, oxygen radius 1.82 Å). In addition, different functional forms are used for VDW interactions in these two models, TAFF (Leonard-Jones 12-6) and MM3 (Buckingham exp-6). It is clear that the coordination scan method underestimates q-values in the current application. Although the method may work with other force field models, we note that there is a fundamental flaw with the approach. The method relies on the use of a model in which the inner-sphere atoms are formally connected to the metal. In such models, each metal-ligand bond stretch interaction is treated with a potential function that has an interaction energy of zero when the bond is at its equilibrium length. These models are useful for predicting structures and examining conformational potential surfaces, but they do not address completely the energetics of bond formation. Thus, while the “coordination scan” method may indicate which coordination number is sterically favored as a function of metal ion radius, it ignores any compensating stabilization that might result from Gd-OH2 bonding interactions. “Strain Threshold” and “Surface Area Threshold” Methods. To overcome the inherent deficiency in the “coordination scan” approach, we chose an alternate way of interpreting the steric energies for a series of Gd(ligand)(O)n complexes. The method is based on the concept that adding a water molecule to the coordination sphere in the absence of any steric hindrance will result in a bonding interaction with a stabilizing energy. If the destabilizing strain energy for adding the next water molecule exceeds an intrinsic stabilization energy threshold, then the water will not be bound. An analogous threshold concept can be applied to the interpretation of Gd surface area data. In other words, there is a minimal space requirement for adding another oxygen atom to the inner sphere. If there is insufficient space, then the water will not be bound. To test these concepts, we optimized a series of Gd(ligand)(O)n complexes, where n ) 1 to q+1, for each ligand in the test set. Incremental strain energies for the sequential addition of oxygen atoms and exposed Gd surface areas are summarized in Table 2. It can be seen that the strain for adding an oxygen atom to the inner sphere gradually increases as the coordination number increases (23). The strain energies for forming the n ) q species range from 5.3 to 7.8 kcal/mol. The strain energies for forming the n ) q+1 species are significantly higher, 11.3 to 23.5 kcal/mol. Thus, there is a threshold energy that lies somewhere between 8 and 11 kcal/mol. Setting a threshold in the middle of this range yields the following criterion that correctly predicts q for all structures in the test set: if the strain energy for adding the next oxygen atom exceeds 9.5 ( 1.5 kcal/mol, then the next oxygen atom will not bind.

Technical Notes Table 2. Strain Energies for the Addition of O Atoms and Exposed Gd VDW Surface Areas Used To Predict q-Values via Threshold Methods complex Gd(EDTA)(O) Gd(EDTA)(O)2 Gd(EDTA)(O)3 Gd(EDTA)(O)4 Gd(NOTA) Gd(NOTA)(O) Gd(NOTA)(O)2 Gd(NOTA)(O)3 Gd(NOTA)(O)4 Gd(DO3A) Gd(DO3A)(O) Gd(DO3A)(O)2 Gd(DO3A)(O)3 Gd(DTPA) Gd(DTPA)(O) Gd(DTPA)(O)2 Gd(DOTA) Gd(DOTA)(O) Gd(DOTA)(O)2 Gd(TTHA) Gd(TTHA)(O) Gd(TTPA) Gd(TTPA)(O)

strain energy, Gd surface predicted observed kcal/mol area, Å q-value q-value 0.4 2.2 5.3 11.3 1.2 7.1 6.1 20.4 4.0 6.4 17.1 7.8 13.3 5.8 21.9 23.4 23.5

12.4 7.7 4.5 2.9 14.2 9.6 6.5 4.5 3.4 9.3 6.3 3.9 2.9 8.2 5.8 4.1 7.1 4.2 4.8 3.5 3.6 3.2 3.1

3

3

3

3

2

2

1

1

1

1

0

0

0

0

Similarly, as the number of atoms in the inner sphere increases the surface area decreases. At n ) q - 1, where there should be sufficient space to allow another bound oxygen atom, Gd surface areas range from 6.3 to 8.2 Å2. At n ) q, where there should not be sufficient space to allow another bound oxygen atom, the Gd surface areas range from 3.2 to 5.8 Å. Thus, there is a threshold surface area that lies near 6.0 Å2. Interestingly, this is exactly the surface area consumed when a single oxygen atom is bound to a bare Gd(III) ion. These observations lead to a second criterion that also correctly predicts q for all structures in the test set: if the exposed Gd surface area is less than 6.0 Å2, then the next oxygen atom will not bind. SUMMARY AND CONCLUSIONS

The reported “Connolly surface area” method (6) is based on the exposed VDW, rather than the Connolly, surface of the Gd ion. We find that while there exists a definite trend between the exposed surface area of the metal ion in a nonhydrated Gd(ligand) complex and the number of water molecules that will bind, the method fails as an accurate predictor of q-value in two out of seven test cases. We have presented a modified approach, the “surface area threshold” method, which predicts all q values in the test set using exposed Gd VDW surface areas from geometry optimized Gd(ligand)(O)n complexes. The “coordination scan” method is force field dependent and systematically underestimates q with our extended MM3 model. Efforts to compensate for an inherent deficiency in the “coordination scan” approach led us to develop an alternate method to apply POS force fields to q prediction. In the “strain threshold” method, q is predicted by evaluating the increase in strain that accompanies successive addition of oxygen atoms to the inner sphere. A water molecule will not be bound when this increase exceeds a threshold energy. Calibration of this method on the test set yields a threshold value that correctly predicts q in all cases. With the MM3 model used here, this value is 9.5 ( 1.5 kcal/mol. Although this threshold will depend on the parameter set, the “strain threshold” method should be applicable with other force

Technical Notes

fields. Calibration with a set of known compounds must be performed to establish the appropriate threshold for the force field used. Finally, this study demonstrates that simple approaches based on steric hindrance can be used to predict observed q values for Gd aminocarboxylate complexes. The predictions are based on thresholds for surface area and strain. These thresholds, which reflect a competition between steric and electronic effects, may vary as a function of the binding sites that are present in the ligand. Binding sites that are more electron donating than amine nitrogen atoms and carboxylate oxygen atoms might make it more difficult to add an inner sphere aqua ligand. This situation would be expected to increase the surface area threshold and decrease the strain energy threshold. It remains to be seen whether the thresholds derived from this set of aminocarboxylate ligands are transferable to complexes bearing other classes of ligands. ACKNOWLEDGMENT

This research was performed at the Pacific Northwest National Laboratory, operated by Battelle for the U.S. Department of Energy (DOE) under contract DE-AC0676RLO 1830 and supported (PNNL) by Grant No. 73759 of the Environmental Management Science Program of the Office of Science, DOE, and (UCB) NIH Grant HL69832. The authors would like to thank Profs. R. D. Hancock and D. E. Reichert for their helpful comments and suggestions. Supporting Information Available: The extended MM3 parameter set and input files for the Gd-aminocarboxylate complexes. This material is available free of charge via the Internet at http://pubs.acs.org/BC. LITERATURE CITED (1) Lauffer, R. B. (1987) Paramagnetic Metal-Complexes as Water Proton Relaxation Agents for NMR Imaging - Theory and Design. Chem. Rev. 87, 901. (2) Caravan, P., Ellison, J. J., McMurry, T. J., and Lauffer, R. B. (1999) Gadolinium(III) Chelates as MRI Contrast Agents: Structure, Dynamics, and Applications. Chem. Rev. 99, 2293. (3) Merbach, A. E., and Toth, E., Eds. (2001) The Chemistry of Contrast Agents in Medical Magnetic Resonance Imaging, Wiley, Chichester. (4) Reichert, D. E., Lewis, J. S., and Anderson, C. J. (1999) Metal Complexes as Diagnostic Tools. Coord. Chem. Rev. 184, 3. (5) (a) Fossheim, R., and Dahl, S. G. (1990) Molecular Structure and Dynamics of Aminopolycarboxylates and their Lanthanide Ion Complexes. Acta Chem. Scand. 44, 696. (b) Fossheim, R., Dugstad, H., and Dahl, S. G. (1991) StructureStability Relationships of Gd(III) Ion Complexes for Magnetic Resonance Imaging. J. Med. Chem. 34, 819. (c) Tan, Y. T., Judson, R. S., Melius, C. F., Toner, J., and Wu G. (1996) Using Molecular Dynamics to Predict Factors Affecting Binding Strength and Magnetic Relaxivity of MRI Contrast Agents. J. Mol. Model. 2, 160. (d) Durand, S., Dognon, J.-P., Guilbaud, P., Rabbe, C., and Wipff, G. (2000) Lanthanide and AlkalineEarth Complexes of EDTA in Water: A Molecular Dynamics Study of Structures and Binding Selectivities. J. Chem. Soc., Perkin 2 705. (e) Chang, C. A., Liu, Y.-L., Chen, C.-Y., and Chou, X.-M. (2001) Ligand Preorganization in Metal Ion Complexation: Molecular Mechanics/Dynamics Kinetics, and Laser-Excited Luminescence Studies of Trivalent Lanthanide Complex Formation with Macrocyclic Ligands TETA and DOTA. Inorg. Chem. 40, 5448. (6) Castonguay, L. A., Treasurywala, A. M., Caulfield, T. J., Jaeger, E. P., and Kellar, K. E. (1999) Prediction of q-Values

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1502 Bioconjugate Chem., Vol. 15, No. 6, 2004 (1998) A Molecular Mechanics (MM396) Force Field for MetalAmide Complexes. Inorg. Chem. 37, 5887. (13) Hay, B. P. (1993) Methods for Molecular Mechanics Modeling of Coordination Compounds. Coord. Chem. Rev. 126, 177. (14) Hay, B. P., Uddin, J., and Firman, T. K. (2004) Eightcoordinate Stereochemistries of U(IV) Catecholate and Aqua Complexes. Polyhedron 23, 145. (15) Hay, B. P. (1991) Extension of Molecular Mechanics to High-Coordinate Metal Complexes. Calculation of the Structures of Aqua and Nitrato Complexes of Lanthanide(III) Metal Ions. Inorg. Chem. 30, 2876. (16) Cundari, T. R., Moody, E. W., and Sommerer, S. O. (1995) Computer-Aided Design of Metallopharmaceuticals: A Molecular Mechanics Force Field for Gadolinium Complexes. Inorg. Chem. 34, 5989. (17) (a) Pascual-Ahuir, J. L. and Silla, E. (1990) GEPOL: An Improved Description of Molecular Surfaces. I. Building the Spherical Surface Set. J. Comput. Chem. 11, 1047. (b) Silla, E., Tunon, I., and Pascual-Ahuir, J. L. (1991) GEPOL: An Improved Description of Molecular Surfaces. II. Computing the Molecular Area and Volume. J. Comput. Chem. 12, 1077. (c) Pascual-Ahuir, J. L., Tunon, I., and Silla, E. (1994) GEPOL: An Improved Description of Molecular Surfaces. III. A New Algorithm for the Computation of a Solvent-Excluding Surface. J. Comput. Chem. 15, 1127.

Technical Notes (18) Clark, M., Cramer, R. D., III., and van Opdenhosch, N. (1989) Validation of the General Purpose Tripose 5.2 Force Field. J. Comput. Chem. 10, 982. (19) Chatterjee, A., Maslen, E. N., and Watson, K. J. (1988) The Effect of the Lanthanoid Contraction on the Nonaaqualanthanoid(III) Tris(trifluoromethanesulfonates. Acta Crystallogr., B 44, 381. (20) Shannon, R. D. (1976) Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides. Acta Crystallogr., A32, 751. (21) (a) Connolly, M. L. (1983) Solvent-Accessible Surfaces of Proteins and Nucleic Acids. Science 221, 709. (b) Connolly, M. L. (1983) Analytical Molecular Surface Calculation. J. Appl. Crystallogr. 16, 548. (22) Hegetschweiler, K., Hancock, R. D., Ghisletta, M., Kradolfer, T., Gramlich, V., and Schmalle, H. W. (1993) 1,3,5Triamino-1,3,5-trideoxy-cis-inosotol, a Ligand with a Remarkable Versatility for Metal Ions. 5. Complex Formation with Magnesium(II), Calcium(II), Strontium(II), Barium(II), and Cadmium(II). Inorg. Chem. 32, 5273. (23) The only exception is with NOTA where the addition of the third oxygen atom occurs with 1.0 kcal/mol less strain than the addition of the second oxygen atom.

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