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1 Gadoliniu(III) Coplexes of Mono- and Diethyl Esters of Monophosphonic Acid Analogue of DOTA as Potential MRI Contrast Agents: Solution Structures and Relaxoetric Studies Petra Lebdušková, a,b Petr Herann, a Lothar Hel,* b Éva Tóth, b,c Jan Kotek, a,d Koen Binneans, d Jakub Rudovský, a Ivan Lukeš,* a and André E. Merbach b a Departent of Inorganic Cheistry, Charles University, Hlavova 030, 840 Prague, Czech Republic. Fax: ; Tel: ; E-ail: lukes@natur.cuni.cz b Laboratoire de chiie inorganique et bioinorganique, Ecole Polytechnique Fédérale de Lausanne, CH- 05 Lausanne, Switzerland. Fax: ; Tel: ; E-ail: lothar.hel@epfl.ch c Centre de biophysique oléculaire, CNRS, rue Charles-Sadron, 4507 Orléans, Cedex, France. d Departent of Cheistry, Katholieke Universiteit Leuven, Celestijnenlaan 00F, B-300 Leuven, Belgiu. Appendix. Equations used in the analysis of 7 O NMR and H NMRD data. Table S: Proton relaxivities (r / M s ) of [Gd(do3ap OEt )(H O)], c(gd III ) = 4.7 M, ph = 6.30, at variable teperature. Table S: Proton relaxivities (r / M s ) of [Gd(do3ap OEt )(H O)], c(gd III ) = 4. M, ph = 6.5, at variable teperature. Table S3: Variable teperature reduced transversal and longitudinal 7 O relaxation rates of [Gd(do3ap OEt )(H O)], c(gd III ) = 79 M, ph = 5.98, P = at 9.4 T. Reference was acidified H O, ph = 6. Table S4: Variable teperature reduced transversal and longitudinal 7 O relaxation rates of [Gd(do3ap OEt )(H O)], c(gd III ) = 36 M, ph = 6., P = at 9.4 T. Reference was acidified H O, ph = 3.7. Figure S. Variable teperature reduced 7 O cheical shifts of [Gd(do3ap OEt )(H O)], c(gd III ) = 36 M, ph=6., P = at 9.4 T. Reference was acidified H O, ph = 3.7. Figure S. Variable teperature reduced 7 O cheical shifts of [Gd(do3ap OEt )(H O)], c(gd III ) = 79 M, ph=5.98, P = at 9.4 T. Reference was acidified H O, ph = 6. Table S5. Fitted paraeters of [Gd(do3ap OEt )(H O)] and [Gd(do3ap OEt )(H O)]. The underlined paraeters were fixed during the fitting. Figure S3: Dependence of the cheical shift of 3 P NMR signals of [Eu(do3ap OEt )H O] on teperature; ph 6.5 Figure S4: Dependence of fraction of TSAP isoer of [Eu(do3ap OEt )(H O)] on ph; easured at 3 C by 3 P NMR Figure S5: Dependence of fraction of TSAP isoer of [Eu(do3ap OEt )(H O)] on ph; easured at 3 C by H NMR Figure S6: Dependence of fraction of TSAP isoer of [Eu(do3ap OEt )(H O)] on ph; easured at 3 C by 3 P NMR. Figure S7: Dependence of fraction of TSAP isoer of [Eu(do3ap OEt )(H O)] on ph; easured at 3 C by H NMR. Figure S8: Teperature dependence of UV-VIS spectra of [Eu(do3ap OEt )(H O)]. Figure S9: Teperature dependence of UV-VIS spectra of [Eu(do3ap OEt )(H O)]. Figure S0: The contact contributions to the 7 O LIS easureents of [Ln(do3ap OEt )(H O)], easured at 9.4 T, 5 C and ph 7. Figure S: H NMRD profile of [Gd(do3ap)(H O)] coplex recorded at 37 C ( ) with fitted line (full line) and calculated contributions fro outer-sphere (dashed line) and secondsphere (dotted line) water.

2 Appendix. 7 O NMR relaxation: Fro the easured 7 O NMR relaxation rates and angular frequencies of the paraagnetic solutions, /T, /T and ω, and of the acidified water reference, /T A, /T A and ω A, one can calculate the reduced relaxation rates, /T r, /T r (Eq. [] and []), where /T, /T are the relaxation rates of the bound water and Δω is the cheical shift difference between bound and bulk water, τ is the ean residence tie or the inverse of the water exchange rate k ex and P is the ole fraction of the bound water., = Tr P T T = + [] A T + τ T OS T + τt +Δω = T r P T T = + [] A τ τ + T +Δω TOS ( ) The ters /T OS and /T OS describe relaxation contributions fro water olecules not directly bound to the paraagnetic centre. In previous studies it has been shown that 7 O outer-sphere relaxation ters due to water olecules freely diffusing on the surface of Gd-polyainocarboxylate coplexes are negligible. For coplexes with phosphate groups relaxation ters due to nd -sphere water olecules can however be iportant for longitudinal relaxation /T r and have therefore to be included. = + = + [3] st nd nd Tr Tr Tr T + τ Tr T + τ T +Δω = = [4] st T r Tr τ τ + T +Δω ( ) First-sphere contribution to 7 O relaxation: The 7 O longitudinal relaxation rates in Gd(III) solutions are the su of the contributions of the dipole-dipole and quadrupolar (in the approxiation developed by Halle for non-extree narrowing conditions) echaniss as expressed by Eq. [6]-[7], where γ S is the electron and γ I is the nuclear gyroagnetic ratio (γ S =.76 0 rad s T, γ I = rad s T ), r GdO is the effective distance between the electron charge and the 7 O nucleus, I is the nuclear spin (5/ for 7 O), χ is the quadrupolar coupling constant and η is an asyetry paraeter: = + [5] T T T dd q μ 0 I S = γ γ S 6 ( S ) 3 J ( ωi; τd) 7 J ( ωs; τd) ; J ( ω; τ) τ dd 5 4π + + = r GdO + T ( ωτ ) τ = d τ + T + e τro 3 π I + 3 η = χ + 0. J ( ωi; τro) J ( ωi; τro) ; Jn ( ω; τ) = τ T q 0 I ( I ) 3 + nωτ ( ) In the transverse relaxation the scalar contribution, /T sc, is doinating, Eq. [8]. /τ s is the su of the exchange rate constant and the electron spin relaxation rate. S( S + ) A = τ [8] S T TSC 3 = + [9] τ τ T S e [6] [7]

3 Second-sphere contribution to 7 O relaxation: nd nd q q = nd st nd st + nd nd T q T q Tdd T q 3τ =C + nd,o nd,o nd,o d d nd dd Tdd + ωτ + ωτ 7τ nd,o nd,o ( I d ) ( S d ) nd,o μ 7 0 h γ γ O S C dd = S S+ nd 6 5 4π r ( GdO ) ( ) 3π I τ 0.8τ ( ) T I I + ωτ + ωτ nd,o nd,o = χ +η 3 + nd q 0 ( ) = + τ τ τ τ O,nd O O g l l τ nd =k nd,o ex + + O,nd di τ T ie nd,o nd,o ( I ) ( I ) [0] [] [] [3] [4] H NMRD: obs The easured longitudinal proton relaxation rate, R is the su of a paraagnetic and a diaagnetic contribution as expressed in Eq. [5], where r is the proton relaxivity: obs d p d 3 R = R + R = R + r Gd + [5] The relaxivity is here given by the su of inner-sphere, second-sphere and outer-sphere contributions: r = r + r + r [6] is,nd os Inner-sphere H relaxation: The inner-sphere ter is given in Eq. [7], where q st is the nuber of inner-sphere water olecules. 3 st q r is = [7] H T + τ The longitudinal relaxation rate of inner-sphere protons, /T H is expressed by Eq. [8], where r GdH is the effective distance between the electron charge and the H nucleus, ω I is the proton resonance frequency and ω S is the Laror frequency of the Gd(III) electron spin. μ0 γ Iγ S = 6 ( ) 3 ( I; d) 7 ( S; H S S + J ω τ + J ω τd) T 5 4π r [8] GdH S τ ( S ) τ dig di J ( ωτ ; di ) = + ; i =, [9] + ωτdig + ωτ di τ = τ + τ + T ; H τ = τ + τ + T ; i =, [0] dig g ie = + H H τ τg τl dig ie The spectral density functions are given by Eq. [9]. [] 3

4 Second-sphere H relaxation: nd nd nd q q T nd,h nd,h dd + τ nd T dd r = τ nd,h nd,h nd,o d d =C nd,h dd + Tdd + ωτ + ωτ 7τ nd,h nd,h ( I d ) ( S d ) nd,h μ 0 h γ γ H S C dd = S S+ nd 6 5 4π r ( GdO ) =k + + nd nd,h ex H τdi τ Tie = + H H τ τg τl ( ) [] [3] [4] [5] [6] Outer-sphere H relaxation: The outer-sphere contribution can be described by Eq. [7] where N A is the Avogadro constant, and J os is its associated spectral density function. 4,5 3N Aπ μ0 γ Sγ I os = + os I e + os S e 405 4π agdh DGdH ( ) 3 ( ω ; ) 7 ( ω ; ) r S S J T J T / τ GdH + iωτgdh + 4 Tje Jos ( ω, Tje ) = Re ; j =, [8] / 3/ τ GdH 4 τ GdH τ GdH + iωτgdh + + iωτgdh + + iωτgdh + T je 9 T je 9 T je agdh τ GdH = [9] DGdH a GdH is the distance of closes approach and D GdH is the diffusion coefficient for the diffusion of a water proton relative to the Gd(III) coplex. Electron spin relaxation: The longitudinal and transverse electronic relaxation rates, /T e and /T e are described by Soloon- Bloebergen-Morgan theory odified by Powell (Eqs. [30]-[3]), where τ V is the correlation tie for the odulation of the zero-field-splitting interaction. ZFS 4 = Δ τ v { 4S( S + ) 3} + [30] T e 5 + ωτ S v + 4ωτ S v ZFS =Δ τ v + [3] T e ωτ S v +.4ωτ S v [7] Teperature dependences of water exchange rates and correlation ties: The exchange rates are supposed to follow the Eyring equation. In Eq. [3] ΔS and ΔH are the entropy and enthalpy of activation for the water exchange process, and k ex 98 is the exchange rate 4

5 at 98.5 K. In Eq. [33] ΔH nd is the enthalpy of activation for the second sphere water exchange process and k nd,98 ex is the corresponding exchange rate at 98 K. 98 kt B ΔS ΔH kex T ΔH kex = = exp = exp [3] τ h R RT 98.5 R 98.5 T nd,98 nd nd kex ΔH [33] kex = exp 98.4 T 98.5 T All correlation ties and the diffusion constant are supposed to obey an Arrhenius law: 98 E exp a τ = τ R T EGdH DGdH = DGdH exp R 98.5 T [34] [35] 5

6 Table S: Proton relaxivities (r / M s ) of [Gd(do3ap OEt )(H O)], c(gd III ) = 4.7 M, ph = 6.30, at variable teperature. ν( H) /MHz 5 C 5 C 37 C 50 C

7 Table S: Proton relaxivities (r / M s ) of [Gd(do3ap OEt )(H O)], c(gd III ) = 4. M, ph = 6.5, at variable teperature. ν( H) /MHz 5 C 5 C 37 C 50 C

8 Table S3: Variable teperature reduced transversal and longitudinal 7 O relaxation rates of [Gd(do3ap OEt )(H O)], c(gd III ) = 79 M, ph = 5.98, P = at 9.4 T. Reference was acidified H O, ph = 6. t / C T / K 000/T / K P T (Gd)/s T (H O)/s T (Gd)/s T (H O)/s ln(/t r ) ln(/t r ) E E E E-04 3.E E E E E E E E E E E E E E E E E E E-03.33E E E-03.03E-0.3E-0.0E E E-03.4E-0.46E E E E-03.45E-0.7E E-03.0E E-03.69E-0.89E E-03.37E Table S4: Variable teperature reduced transversal and longitudinal 7 O relaxation rates of [Gd(do3ap OEt )(H O)], c(gd III ) = 36 M, ph = 6., P = at 9.4 T. Reference was acidified H O, ph = 3.7. t / C T / K 000/T / K P T (Gd)/s T (H O)/s T (Gd)/s T (H O)/s ln(/t r ) ln(/t r ) E E E-03.40E E E E E-03.3E E E E E-03.9E E E E E-03.7E E E E-03 7.E-03.3E E E E E-03.4E E E E E-03.5E E E-04.05E-0.4E-0.43E E E-04.3E-0.4E-0.07E-03.07E E-04.56E-0.69E E-03.9E E-04.83E-0.95E E-03.34E E-04.09E-0.4E E-03.5E

9 Figure S. Variable teperature reduced 7 O cheical shifts of [Gd(do3ap OEt )(H O)], c(gd III ) = 36 M, ph=6., P = at 9.4 T. Reference was acidified H O, ph = ω r / 0 6 rad s /T / K - Figure S. Variable teperature reduced 7 O cheical shifts of [Gd(do3ap OEt )(H O)], c(gd III ) = 79 M, ph=5.98, P = at 9.4 T. Reference was acidified H O, ph = 6. 9

10 ω r / 0 6 rad s /T / K - Table S5. Fitted paraeters of [Gd(do3ap OEt )(H O)] and [Gd(do3ap OEt )(H O)]. The underlined paraeters were fixed during the fitting. Paraeter [Gd(do3ap OEt )(H O)] [Gd(do3ap OEt )(H O)] k 98 ex [0 6 s ] 4.4±0.3 0±5 ΔH [kj ol ] 56.8± 6.4±5 ΔS [J ol K ] +7.7± ±0.6 A/ħ [0 6 rad s ] τ 98 R (O) [ps] 77±8 84±9 Ε R [kj ol ] 0 τ 98 V [ps].4±.5 8.7±. Ε V [kj ol ] Δ [0 0 s ] ±0.07 D 98 GdH [0 0 s ] 5±3 5± Ε DGdH [kj ol ] 8± ± δg L [0 ].7 3.3±0. τ 98 R (H)/ τ 98 R (O) 0.77± ±0.0 r GdO [Å].5.5 r GdH [Å] r GdHouter [Å] χ(+η /3) / [MHz] q q nd 98 τ M nd [ps] ΔH nd [kj ol ]

11 r nd GdH [Å] r nd GdO [Å] Figure S3: Dependence of the cheical shift of 3 P NMR signals of [Eu(do3ap OEt )H O] on teperature; ph SAP SAP TSAP 3 TSAP 4 44 δ 3 P / pp t / C Figure S4: Dependence of fraction TSAP isoer of [Eu(do3ap OEt )(H O)] on ph; easured at 3 C by 3 P NMR /(+M) ph Figure S5: Dependence of fraction TSAP isoer of [Eu(do3ap OEt )(H O)] on ph; easured at 3 C by H NMR

12 /(+M) ph Figure S6: Dependence of fraction TSAP isoer of [Eu(do3ap OEt )(H O)] on ph; easured at 3 C by 3 P NMR. /(+M) ph

13 Figure S7: Dependence of fraction TSAP isoer of [Eu(do3ap OEt )(H O)] on ph; easured at 3 C by H NMR. /(+M) ph 3

14 Figure S8: Teperature dependence of UV-Vis spectra of [Eu(do3ap OEt )(H O)]..70E-0.50E-0.30E-0 5 C 5 C 45 C 65 C 80 C.0E E E E E-03.00E E Figure S9: Teperature dependence of UV-Vis spectra of [Eu(do3ap OEt )(H O)]..30E-0.0E-0 0 C 5 C 40 C 55 C 70 C 80 C 9.00E E E E-03.00E E

15 Figure S0: The contact contributions to the 7 O LIS easureents of [Ln(do3ap OEt )(H O)], easured at 9.4 T, 5 C and ph Ho Tb 0 Dy Yb Er -50 Nd Δ'/<CD> Eu <Sz>/<CD> Figure S: H NMRD profile of [Gd(do3ap)(H O)] coplex recorded at 37 C ( ) with fitted line (full line) and calculated contributions fro outer-sphere (dotted line) and secondsphere (dashed line) water. 5

16 References for equations. T. J. Swift, R. E. Connick, J. Che. Phys., 96, 37, 307. J. R. Zierann, W. E. Brittin, J. Phys. Che., 957, 6, Z. Luz, S. Meiboo, J. Che. Phys., 964, 40, J. H. Freed, J. Che. Phys., 978, 68, S. H. Koenig, R. D. Brown III, Prog. Nucl. Magn. Reson. Spectrosc., 99,,