Phosphinic derivative of DTPA conjugated to a G5 PAMAM dendrimer: an. Supplementary information

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1 Phosphinic derivative of DTPA conjugated to a G5 PAMAM dendrier: an 17 O and 1 H relaxation study of its Gd(III) coplex Petra Lebdušková, ab Angélique Sour, b Lothar Hel,* b Éva Tóth, bc Jan Kotek, a Ivan Lukeš * a and André E. Merbach b a Departent of Inorganic Cheistry, Charles University, Hlavova 030, 1840 Prague, Czech Republic. Fax: ; Tel: ; E-ail: lukes@natur.cuni.cz b Institut des Sciences et Ingénierie Chiiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland. Fax: ; Tel: ; E-ail: lothar.hel@epfl.ch c Centre de biophysique oléculaire, CNRS, rue Charles-Sadron, Orléans, Cedex, France. Suppleentary inforation Appendix. Equations used in the analysis of 17 O NMR and 1 H NMRD data. Table S1. Proton relaxivities (r 1 / M -1 s -1 ) of G5-(Gd(DTTAP)) 63, c(gd III )=5.3 M, ph=6.5, at variable teperature. Table S. Proton relaxivities (r 1 / M -1 s -1 ) of [Gd(DTTAP-bz-NH )(H O)] -, c(gd III )=4. M, ph=6.75, at variable teperature. Table S3. Proton relaxivities (r 1 / M -1 s -1 ) of [Gd(DTTAP-bz-NO )(H O)] -, c(gd III )=3.8 M, ph=6.59, at variable teperature. Table S4. Variable teperature reduced transverse and longitudinal 17 O relaxation rates of G5- (Gd(DTTAP)) 63, c(gd III )=39 M, ph=5.69, P = at 9.4 T. Reference was G5-(Y(DTTAP)) 63, c(y III )=34 M, ph=5.83. Table S5. Variable teperature reduced transverse and longitudinal 17 O relaxation rates of G5- (Gd(DTTAP)) 63, c(gd III )=39 M, ph=5.69, P = at 4.7 T. Reference was G5-(Y(DTTAP)) 63, c(y III )=34 M, ph=5.83. Table S6. Variable teperature reduced transverse and longitudinal 17 O relaxation rates of [Gd(DTTAP-bz-NH )(H O)] -, c(gd III )=46 M, ph=5.51, P = at 9.4 T. Reference was acidified H O, ph=3.3. Table S7. Variable teperature reduced transverse and longitudinal 17 O relaxation rates of [Gd(DTTAP-bz-NO )(H O)] -, c(gd III )=3 M, ph=5.91, P = at 9.4 T. Reference was acidified H O, ph=3.3. Table S8. Calculation of the nuber of chelating groups per dendrier. Figure S1. Variable teperature reduced 17 O cheical shifts of [Gd(DTTAP-bz-NO )(H O)] -, c(gd III )=3 M, ph=5.91, P = at 9.4 T. Reference was acidified H O, ph=3.3. Figure S. Variable teperature reduced 17 O cheical shifts of [Gd(DTTAP-bz-NH )(H O)] -, c(gd III )=46 M, ph=5.51, P = at 9.4 T. Reference was acidified H O, ph=3.3. Figure S3. Variable teperature reduced 17 O cheical shifts of G5-(Gd(DTTAP)) 63, c(gd III )=39 M, ph=5.69, P = at 4.7 T and 9.4 T. Reference was G5-(Y(DTTAP)) 63, c(y III )=34 M, ph=5.83. Table S9. Fitted paraeters of G5-(Gd(DTTAP)) 63. Table S10. Fitted paraeters of [Gd(DTTAP-bz-NO )(H O)] - and [Gd(DTTAP-bz-NH )(H O)] -. The underlined paraeters were fixed during the fitting. 1

2 Equations. 17 O NMR relaxation: Fro the easured 17 O NMR relaxation rates and angular frequencies of the paraagnetic solutions, 1/T 1, 1/T and ω, and of the acidified water reference, 1/T 1A, 1/T A and ω A, one can calculate the reduced relaxation rates, 1/T 1r, 1/T r (Eq. [1] and []), where 1/T 1, 1/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. 1, = T1r P T1 T = + [1] 1A T1 + τ T1 OS T + τ T +Δω 1 T P T T + +Δ T S 1 1 = = r A τ τ ω O ( T ) The ters 1/T 1OS and 1/T OS describe relaxation contributions fro water olecules not directly bound to the paraagnetic centre. In previous studies it has been shown that 17 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 1/T 1r and have therefore to be included. 1 1 = + = + [3] 1st nd nd T1r T1r T1r T1 + τ T1r 1 1 T + τ T +Δω = = [4] 1st 1 1 Tr T r τ τ + T +Δω ( ) First sphere contribution to 17 O relaxation: The 17 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 = rad s -1 T -1, γ I = rad s -1 T -1 ), r GdO is the effective distance between the electron charge and the 17 O nucleus, I is the nuclear spin (5/ for 17 O), χ is the quadrupolar coupling constant and η is an asyetry paraeter: = + [5] T T T 1 1dd 1q 0 I S 6 rgdo 1 = S( S 1) 3 J ( I; d1) 7 J ( S; d) ; J ( ; ) T1 dd 15 μ γ γ ω τ ω τ ω τ τ 4π + + = [6] 1 + ( ωτ ) 1 τ = d1 τ + T + 1e τr O 1 3π I + 3 η τ = χ J1( ωi; τro) J ( ωi; τro) ; Jn ( ω; τ) = [7] T1 q 10 I ( I 1) ( nωτ ) In the transverse relaxation the scalar contribution, 1/T sc, is doinating, Eq. [8]. 1/τ s1 is the su of the exchange rate constant and the electron spin relaxation rate. 1 1 S( S + 1) A = τ [8] S1 T TSC 3 = + [9] τ τ S1 T1 e []

3 For slowly rotating species with internal degrees of freedo, the spectral density functions J are described the Lipari-Szabo approach. 3,4 In this odel we distinguish two statistically independent otions; a rapid local otion with a correlation tie τ l and a slower global otion with a correlation tie τ g. Supposing the global olecular reorientation is isotropic, the relevant spectral density functions are expressed as in Eq. [10]-[13], where the general order paraeter S describes the degree of spatial restriction of the local otion. If the local otion is isotropic, S =0; if the rotational dynaics is only governed by the global otion, S =1. S τ ( 1 S ) τ dig di J ( ωτ ; di ) = + 1+ ωτdig 1+ ωτ di [10] 1 τ τ τ 1 O T τ τ τ T ; i = 1, [11] dig g ie = + O O τ τ τ J n ( ω) g l S τ g = ( nωτ g ) 1 + di ie O ( 1 S ) τ O ( nωτ ) [1] [13] Second sphere contribution to 17 O relaxation: nd nd 1 q 1 q 1 1 = nd 1st nd 1st + nd nd T1 q T1 q T1dd T 1q 1 3τ =C + nd,o nd,o nd,o d1 d nd dd T1dd 1+ ωτ 1+ ωτ 7τ nd,o nd,o ( I d1 ) ( S d ) nd,o μ 17 0 h γ γ O S C dd = S S+1 nd π r ( GdO ) ( ) 1 3π I τ 0.8τ ( ) T I I 1 1+ ωτ 1+ ωτ nd,o nd,o = χ 1+η 3 + nd 1q 10 ( ) = + 1 τ τ τ τ O,nd O O g l l τ τ nd =k nd,o ex + + O,nd di T ie [14] nd,o nd,o ( I ) ( I ) [15] [16] [17] [18] 1 H NMRD: obs The easured longitudinal proton relaxation rate, R 1 is the su of a paraagnetic and a diaagnetic contribution as expressed in Eq. [19], where r 1 is the proton relaxivity: obs d p d 3 R = R + R = R + r Gd + [19] 1 1 The relaxivity is here given by the su of inner sphere, second sphere and outer sphere contributions: r = r + r + r [0] 1 1is 1,nd 1os Inner sphere 1 H relaxation: The inner sphere ter is given in Eq. [1], where q 1st is the nuber of inner sphere water olecules. 5 3

4 1st 1 q 1 r1 is = [1] H T1 + τ The longitudinal relaxation rate of inner sphere protons, 1/T H 1 is expressed by Eq. [], where r GdH is the effective distance between the electron charge and the 1 H nucleus, ω I is the proton resonance frequency and ω S is the Laror frequency of the Gd(III) electron spin. 1 μ0 γ Iγ S = S 6 ( S 1) 3 J( I; d1) 7 J( S; H + ω τ + ω τd ) T 15 4π r [] 1 GdH ( 1 S ) S τ τ dig di J ( ωτ ; di ) = + ; i = 1, [3] 1+ ωτdig 1+ ωτ di 1 τ = τ + τ + T ; 1 H τ = τ + τ + T ; i = 1, [4] dig g ie = + H H τ τg τl dig ie The spectral density functions are given by Eq. [3]. Second sphere 1 H relaxation: [5] nd nd nd 1 q 1 1 q 1 1 T nd,h nd,h 1dd + τ nd T 1dd r = τ nd,h nd,h nd,o d1 d =C nd,h dd + T1dd 1+ ωτ 1+ ωτ 7τ nd,h nd,h ( I d1 ) ( S d ) nd,h μ 1 0 h γ γ H S C dd = S S+1 nd π r ( GdO ) =k + + nd nd,h ex H τdi τ Tie = + H H τ τg τl ( ) [6] [7] [8] [9] [30] Outer sphere 1 H relaxation: The outer-sphere contribution can be described by Eq. [31] where N A is the Avogadro constant, and J os is its associated spectral density function. 6,7 3N Aπ μ0 γ Sγ I 1os = + os I 1e + os S e 405 4π agdh DGdH ( 1) 3 ( ω ; ) 7 ( ω ; ) r S S J T J T [31] 1/ 1 τ GdH 1+ iωτgdh + 4 Tje Jos ( ω, Tje ) = Re ; j = 1, [3] 1/ 3/ τ GdH 4 τ GdH 1 τ GdH 1+ iωτgdh + + iωτgdh + + iωτ GdH + T je 9 T je 9 T je agdh τ GdH = [33] 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. 4

5 Electron spin relaxation: The longitudinal and transverse electronic relaxation rates, 1/T 1e and 1/T e are described by Soloon- Bloebergen-Morgan theory odified by Powell (Eqs. [34]-[35]), where τ V is the correlation tie for the odulation of the zero-field-splitting interaction. ZFS { 4S( S 1) 3} = Δ τ v + + T1 e ωsτv 1 + 4ωSτv ZFS =Δ τ v + T e ωSτv ω S τ v [34] [35] Teperature dependences of water exchange rates and correlation ties: The exchange rates are supposed to follow the Eyring equation. In Eq. [36] ΔS and ΔH are the entropy and enthalpy of activation for the water exchange process, and k 98 ex is the exchange rate at K. In Eq. [37] 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 kt B ΔS ΔH kex T ΔH 1 1 kex = = exp = exp [36] τ h R RT R T nd,98 nd nd kex ΔH 1 1 [37] kex = exp T T All correlation ties and the diffusion constant are supposed to obey an Arrhenius law: 98 E 1 1 exp a τ = τ R T [38] 98 EGdH 1 1 DGdH = DGdH exp R T [39] 5

6 Table S1: Proton relaxivities (r 1 / M -1 s -1 ) of G5-(Gd(DTTAP)) 63, c(gd III )=5.3 M, ph=6.5, at variable teperature. ν ( 1 H)/MHz 5 C 15 C 5 C 37 C 50 C

7 Table S: Proton relaxivities (r 1 / M -1 s -1 ) of [Gd(DTTAP-bz-NH )(H O)] -, c(gd III )=4. M, ph=6.75, at variable teperature. ν ( 1 H)/MHz 5 C 5 C 37 C 50 C

8 Table S3: Proton relaxivities (r 1 / M -1 s -1 ) of [Gd(DTTAP-bz-NO )(H O)] -, c(gd III )=3.8 M, ph=6.59, at variable teperature. ν ( 1 H)/MHz 5 C 5 C 37 C 50 C

9 Table S4: Variable teperature reduced transverse and longitudinal 17 O relaxation rates of G5-(Gd(DTTAP)) 63, c(gd III )=39 M, ph=5.69, P = at 9.4 T. Reference was G5-(Y(DTTAP)) 63, c(y III )=34 M, ph=5.83. t / C T / K 1000/T / K -1 T 1 (Gd)/s T 1 (Y)/s T (Gd)/s T (Y)/s ln(1/t 1r ) ln(1/t r ) E-03.80E E-04.00E E E E-04.47E E E E E E E E E E E E E E E E E E E E E E E E E E E-0.49E E E E E E Table S5: Variable teperature reduced transverse and longitudinal 17 O relaxation rates of G5-(Gd(DTTAP)) 63, c(gd III )=39 M, ph=5.69, P = T. Reference was G5-(Y(DTTAP)) 63, c(y III )=34 M, ph=5.83. t / C T / K 1000/T / K -1 T 1 (Gd)/s T 1 (Y)/s T (Gd)/s T (Y)/s ln(1/t 1r ) ln(1/t r ) E-03.68E E E E E E-04.30E E E E-04.67E E E E E E E E E E E E E E E E E E E E E E E E E E E-0.7E E E E E E at 9

10 Table S6: Variable teperature reduced transverse and longitudinal 17 O relaxation rates of [Gd(DTTAP-bz-NH )(H O)] -, c(gd III )=46 M, ph=5.51, P = at 9.4 T. Reference was acidified H O, ph=3.3. t / C T / K 1000/T / K -1 T 1 (Gd)/s T 1 (H O)/s T (Gd)/s T (H O)/s ln(1/t 1r ) ln(1/t r ) E E E E E E E E E E E E E E E E E E E E E E-0 1.9E E E E E E E E-0.14E E E E-0.56E E E E E E E-0.5E-0 5.9E-03.5E Table S7: Variable teperature reduced transverse and longitudinal 17 O relaxation rates of [Gd(DTTAP-bz-NO )(H O)] -, c(gd III )=3 M, ph=5.91, P = at 9.4 T. Reference was acidified H O, ph=3.3. t / C T / K 1000/T / K -1 T 1 (Gd)/s T 1 (H O)/s T (Gd)/s T (H O)/s ln(1/t 1r ) ln(1/t r ) E E E E E E E E E E E E E E E E E E-0 1.0E E E E E E E E-0.09E E E E-0.45E E E E-0 3.0E E E E E E E-0.5E E-03.5E

11 Table S8. Calculation of the nuber of chelating groups per dendrier. G5-(Gd(DTTAP)) 63 n = nuber of ols of chelate per gra of product obtained fro coplexoetric titration Total percentage of C obtained fro 48.9 eleental analysis Percentage of carbon in the chelate 4.9 (DTTAP-bz-NCS = C 1 H 9 N 4 O 10 S) calculated fro n Percentage of carbon in PAMAM skeleton = 4.0 Forula of PAMAM skeleton G5-(NH ) 18 C 16 H 58 N 506 O 5 x = nuber of chelate bound on the dendrier 63 Percentage of substituted aino groups 49% Total percentage of N calculated by using x 16.6 Total percentage of N obtained by eleental analysis 17.3 Total percentage of S calculated by using x 3.1 Total percentage of S obtained by eleental analysis.8 Total percentage of P calculated by using x 3.0 Total percentage of P obtained by eleental analysis.7 Figure S1. Variable teperature reduced 17 O cheical shifts of [Gd(DTTAP-bz-NO )(H O)] -, c(gd III )=3 M, ph=5.91, P = at 9.4 T. Reference was acidified H O, ph=3.3. x10 5 1x x10 5 -x10 5 ω r / rad s -1-3x10 5-4x10 5-5x10 5-6x10 5-7x10 5-8x /T / K -1 11

12 Figure S. Variable teperature reduced 17 O cheical shifts of [Gd(DTTAP-bz-NH )(H O)] -, c(gd III )=46 M, ph=5.51, P = at 9.4 T. Reference was acidified H O, ph=3.3. x10 5 1x x10 5 ω r / rad s -1 -x10 5-3x10 5-4x10 5-5x10 5-6x10 5-7x10 5-8x /T / K -1 Figure S3. Variable teperature reduced 17 O cheical shifts of G5-(Gd(DTTAP)) 63, c(gd III )=39 M, ph=5.69, P = at 4.7 T ( ) and 9.4 T ( ). Reference was G5-(Y(DTTAP)) 63, c(y III )=34 M, ph=5.83. x10 5 1x ω r / rad s -1-1x10 5 -x10 5-3x10 5-4x10 5-5x10 5-6x /T / K -1 1

13 Table S9. Fitted paraeters of G5-(Gd(DTTAP)) 63. The underlined paraeters were fixed during the fitting. Paraeter G5-(Gd(DTTAP)) 63 k 98 ex [10 6 s -1 ] 5.0±0. ΔH [kj ol -1 ] 56.±1.0 ΔS [J ol -1 K -1 ] +71.9±3 A/ħ [10 6 rad s -1 ] -3.8 τ 98 go [ps] 4417±340 Ε go [kj ol -1 ] 1± τ 98 lo [ps] 71±3 Ε lo [kj ol -1 ] 1± S 0.8±0.01 τ 98 V [ps] 1± Ε V [kj ol -1 ] 5.5±5.4 Δ [10 0 s - ] 0.6±0.11 δg L [10 - ] 1.7±0.1 r GdO [Å].5 r GdHouter [Å] 3.5 χ(1+η /3) 1/ [MHz] 7.58 q 1 q nd 98 τ M nd [ps] 50 ΔH nd [kj ol -1 ] 35.0 r nd GdH [Å] 3.5 r nd GdO [Å]

14 Table S10. Fitted paraeters of [Gd(DTTAP-bz-NO )(H O)] - and [Gd(DTTAP-bz-NH )(H O)] -. The underlined paraeters were fixed during the fitting. Paraeter [Gd(DTTAP-bz-NH )(H O)] - [Gd(DTTAP-bz-NO )(H O)] - k 98 ex [10 6 s -1 ] 8.9± ±0.6 ΔH [kj ol -1 ] 48.1±3 48.5± ΔS [J ol -1 K -1 ] +49.8± ±8 A/ħ [10 6 rad s -1 ] τ 98 RO [ps] 116± 117±10 Ε R [kj ol -1 ] 0.5±0.8 18±1 τ 98 V [ps] 8.± ±0.4 Ε V [kj ol -1 ] 1 1 Δ [10 0 s - ] 0.403± ±0.01 D 98 GdH [10-10 s -1 ] 5± 5± Ε DGdH [kj ol -1 ] 30±1 30±1 δg L [10 - ] 3.3±0.6.8±0.5 τ RH / τ RO 0.81± ±0.08 r GdO [Å].5.5 r GdH [Å] r GdHouter [Å] χ(1+η /3) 1/ [MHz] q 1 1 q nd 98 τ M nd [ps] ΔH nd [kj ol -1 ] r nd GdH [Å] r nd GdO [Å] References for equations. 1 T. J. Swift, R. E. Connick, J. Che. Phys., 196, 37, 307. J. R. Zierann, W. E. Brittin, J. Phys. Che., 1957, 61, G. Lipari, S. Szabó, J. A. Che. Soc., 198, 104, G. Lipari, S. Szabó, J. A. Che. Soc., 198, 104, Z. Luz, S. Meiboo, J. Che. Phys., 1964, 40, J. H. Freed, J. Che. Phys., 1978, 68, S. H. Koenig, R. D. Brown III, Prog. Nucl. Magn. Reson. Spectrosc., 1991,,