Phosphinic derivative of DTPA conjugated to a G5 PAMAM dendrimer: an
17
O and 1H relaxation study of its Gd(III) complex
Petra Lebdušková, ab Angélique Sour,b Lothar Helm,*b Éva Tóth, bc Jan Kotek, a Ivan Lukeš *a and
André E. Merbachb
a
Department of Inorganic Chemistry, Charles University, Hlavova 2030, 12840 Prague, Czech Republic.
Fax: +420 2 2195 1253; Tel: +420 2 2195 1259; E-mail: [email protected]
b
Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne,
Switzerland. Fax: +41 21 693 98 75; Tel: +41 21 693 98 76; E-mail: [email protected]
c
Centre de biophysique moléculaire, CNRS, rue Charles-Sadron, 45071 Orléans, Cedex 2, France.
Supplementary information
Appendix. Equations used in the analysis of 17O NMR and 1H NMRD data.
Table S1. Proton relaxivities (r1 / mM-1s-1) of G5-(Gd(DTTAP))63, c(GdIII)=5.3 mM, pH=6.25, at
variable temperature.
Table S2. Proton relaxivities (r1 / mM-1s-1) of [Gd(DTTAP-bz-NH2)(H2O)]2-, c(GdIII)=4.2 mM,
pH=6.75, at variable temperature.
Table S3. Proton relaxivities (r1 / mM-1s-1) of [Gd(DTTAP-bz-NO2)(H2O)]2-, c(GdIII)=3.8 mM,
pH=6.59, at variable temperature.
Table S4. Variable temperature reduced transverse and longitudinal 17O relaxation rates of G5(Gd(DTTAP))63, c(GdIII)=39 mM, pH=5.69, Pm=7.95·10-4 at 9.4 T. Reference was G5-(Y(DTTAP))63,
c(YIII)=34 mM, pH=5.83.
Table S5. Variable temperature reduced transverse and longitudinal 17O relaxation rates of G5(Gd(DTTAP))63, c(GdIII)=39 mM, pH=5.69, Pm=7.95·10-4 at 4.7 T. Reference was G5-(Y(DTTAP))63,
c(YIII)=34 mM, pH=5.83.
Table S6. Variable temperature reduced transverse and longitudinal 17O relaxation rates of
[Gd(DTTAP-bz-NH2)(H2O)]2-, c(GdIII)=46 mM, pH=5.51, Pm=8.19·10-4 at 9.4 T. Reference was
acidified H2O, pH=3.3.
Table S7. Variable temperature reduced transverse and longitudinal 17O relaxation rates of
[Gd(DTTAP-bz-NO2)(H2O)]2-, c(GdIII)=32 mM, pH=5.91, Pm=5.73·10-4 at 9.4 T. Reference was
acidified H2O, pH=3.3.
Table S8. Calculation of the number of chelating groups per dendrimer.
Figure S1. Variable temperature reduced 17O chemical shifts of [Gd(DTTAP-bz-NO2)(H2O)]2-,
c(GdIII)=32 mM, pH=5.91, Pm=5.73·10-4 at 9.4 T. Reference was acidified H2O, pH=3.3.
Figure S2. Variable temperature reduced 17O chemical shifts of [Gd(DTTAP-bz-NH2)(H2O)]2-,
c(GdIII)=46 mM, pH=5.51, Pm=8.19·10-4 at 9.4 T. Reference was acidified H2O, pH=3.3.
Figure S3. Variable temperature reduced 17O chemical shifts of G5-(Gd(DTTAP))63, c(GdIII)=39 mM,
pH=5.69, Pm=7.95·10-4 at 4.7 T and 9.4 T. Reference was G5-(Y(DTTAP))63, c(YIII)=34 mM,
pH=5.83.
Table S9. Fitted parameters of G5-(Gd(DTTAP))63.
Table S10. Fitted parameters of [Gd(DTTAP-bz-NO2)(H2O)]2- and [Gd(DTTAP-bz-NH2)(H2O)]2-.
The underlined parameters were fixed during the fitting.
1
Equations.
17
O NMR relaxation:
From the measured 17O NMR relaxation rates and angular frequencies of the paramagnetic solutions,
1/T1, 1/T2 and ω, and of the acidified water reference, 1/T1A, 1/T2A and ωA, one can calculate the
reduced relaxation rates, 1/T1r, 1/T2r (Eq. [1] and [2]), where 1/T1m, 1/T2m are the relaxation rates of the
bound water and Δωm is the chemical shift difference between bound and bulk water, τm is the mean
residence time or the inverse of the water exchange rate kex and Pm is the mole fraction of the bound
water. 1,2
1
1 ⎡1
1 ⎤
1
1
[1]
=
−
=
+
⎢
⎥
T1r Pm ⎣ T1 T1 A ⎦ T1m + τ m T1OS
1
1 ⎡1
1 ⎤ 1 T2−m2 + τ m−1T2−m1 + Δωm2
1
=
−
=
+
T2 r Pm ⎢⎣ T2 T2 A ⎥⎦ τ m (τ −1 + T −1 )2 + Δω 2 T2OS
2m
m
m
[2]
The terms 1/T1OS and 1/T2OS describe relaxation contributions from water molecules not directly bound
to the paramagnetic centre. In previous studies it has been shown that 17O outer sphere relaxation
terms due to water molecules freely diffusing on the surface of Gd-polyaminocarboxylate complexes
are negligible. For complexes with phosphate groups relaxation terms due to 2nd sphere water
molecules can however be important for longitudinal relaxation 1/T1r and have therefore to be
included.
1
1
1
1
1
[3]
= 1st + 2 nd =
+
T1r
T1r
T1r
T1m + τ m T12r nd
1
1
1 T2−m2 + τ m−1T2−m1 + Δωm2
= 1st =
T2 r
T2 r
τ m (τ −1 + T −1 )2 + Δω 2
m
2m
[4]
m
First sphere contribution to 17O relaxation:
The 17O longitudinal relaxation rates in Gd(III) solutions are the sum of the contributions of the
dipole-dipole and quadrupolar (in the approximation developed by Halle for non-extreme narrowing
conditions) mechanisms as expressed by Eq. [6]-[7], where γS is the electron and γI is the nuclear
gyromagnetic ratio (γS = 1.76×1011 rad·s-1·T-1, γI =-3.626×107 rad·s-1·T-1), rGdO is the effective distance
between the electron charge and the 17O nucleus, I is the nuclear spin (5/2 for 17O), χ is the
quadrupolar coupling constant and η is an asymmetry parameter:
1
1
1
[5]
=
+
T1m T1dd T1q
2
1
2 ⎛ μ ⎞ = 2γ I2γ S2
τ
S ( S + 1) ⎣⎡3J (ωI ;τ d 1 ) + 7 J (ωS ;τ d 2 ) ⎦⎤ ; J (ω;τ ) =
= ⎜ 0⎟
2
6
T1dd 15 ⎝ 4π ⎠ rGdO
1 + (ωτ )
1
τ d1
=
1
τm
+
[6]
1
1
+
T1e τ RO
1
3π 2 2 I + 3
η2 ⎞
2 ⎛
=
+
χ
1
⎜
⎟ ⎡0.2 J 1 (ωI ;τ RO ) + 0.8 J 2 (ωI ;τ RO ) ⎤⎦ ;
T1q
10 I 2 ( 2 I − 1) ⎝
3 ⎠⎣
J n (ω ;τ ) =
τ
2
1 + ( nωτ )
[7]
In the transverse relaxation the scalar contribution, 1/T2sc, is dominating, Eq. [8]. 1/τs1 is the sum of the
exchange rate constant and the electron spin relaxation rate.
2
S ( S + 1) ⎛ A ⎞
1
1
[8]
≅
=
⎜ ⎟ τ S1
T2 m T2 SC
3
⎝=⎠
1
1
1
[9]
= +
τ S1 τ m T1e
2
For slowly rotating species with internal degrees of freedom, the spectral density functions J are
described the Lipari-Szabo approach. 3,4 In this model we distinguish two statistically independent
motions; a rapid local motion with a correlation time τl and a slower global motion with a correlation
time τg. Supposing the global molecular reorientation is isotropic, the relevant spectral density
functions are expressed as in Eq. [10]-[13], where the general order parameter S2 describes the degree
of spatial restriction of the local motion. If the local motion is isotropic, S2=0; if the rotational
dynamics is only governed by the global motion, S2=1.
⎛ S 2τ dig
(1 − S 2 )τ di ⎞⎟
[10]
J (ω;τ di ) = ⎜
+
2
⎜ 1 + ω 2τ dig
1 + ω 2τ di2 ⎟
⎝
⎠
1
1
1
1
1
1 1
1 ;
; i = 1,2
[11]
= + O+
=
+ +
τ di τ m τ
Tie
τ dig τ m τ g Tie
1
τ
O
=
1
τg
+
1
[12]
τ lO
⎛
1 − S 2 )τ O ⎞
S 2τ g
(
⎜
⎟
J n (ω ) =
+
⎜ 1 + ( nωτ )2 1 + ( nωτ O )2 ⎟
g
⎝
⎠
[13]
Second sphere contribution to 17O relaxation:
1
q 2nd 1
q 2nd
≅ 1st 2nd = 1st
2nd
T1
q T1m
q
⎛ 1
1
⎜⎜ 2nd + 2nd
T
T
1q
⎝ 1dd
[14]
⎞
⎟⎟
⎠
⎛
2nd,O
2nd,O
3τ d1
7τ d2
1
2nd,O ⎜
=
C
+
dd
2
2nd
2nd,O
⎜ 1 + ω τ 2nd,O
T1dd
1 + ωS τ d2
I d1
⎝
2
2 2
2
2 ⎛ μ ⎞ h γ 17 O γ S
2nd,O
Cdd
= ⎜ 0⎟
S ( S + 1)
2nd 6
15 ⎝ 4π ⎠ rGdO
(
)
(
(
)
)
⎛
1
3π 2 2I + 3
0.2τ 2nd,O
=
χ 2 1+ η2 3 ⎜
2nd
2
⎜ 1 + ω τ 2nd,O
10 I ( 2I − 1)
T1q
I
⎝
(
1
τ
O,2nd
1
τ di2nd,O
=
[15]
⎞
⎟
2
⎟
⎠
)
(
)
2
+
0.8τ 2nd,O
(
1 + 2ω I τ 2nd,O
1
τ O,2nd
+
[16]
[17]
1
1
1
+
≅ O
τ g τ Ol
τl
2nd
= k ex
+
)
⎞
⎟
2
⎟
⎠
[18]
1
Tie
1
H NMRD:
The measured longitudinal proton relaxation rate, R1obs is the sum of a paramagnetic and a diamagnetic
contribution as expressed in Eq. [19], where r1 is the proton relaxivity:
[19]
R1obs = R1d + R1p = R1d + r1 ⎡⎣Gd 3+ ⎤⎦
The relaxivity is here given by the sum of inner sphere, second sphere and outer sphere contributions:
[20]
r1 = r1is + r1,2 nd + r1os
Inner sphere 1H relaxation:
The inner sphere term is given in Eq. [21], where q1st is the number of inner sphere water molecules. 5
3
1
q1st
1
[21]
×
× H
1000 55.55 T1m + τ m
The longitudinal relaxation rate of inner sphere protons, 1/T1mH is expressed by Eq. [22], where rGdH is
the effective distance between the electron charge and the 1H nucleus, ωI is the proton resonance
frequency and ωS is the Larmor frequency of the Gd(III) electron spin.
2
1
2 ⎛ μ0 ⎞ =2γ I2γ S2
[22]
S ( S + 1) ⎡⎣3J (ωI ;τ d 1 ) + 7 J (ωS ;τ d 2 ) ⎤⎦
=
⎜
⎟
6
T1Hm 15 ⎝ 4π ⎠ rGdH
r1is =
⎛ S 2τ dig
(1 − S 2 )τ di ⎞⎟ ; i = 1,2
J (ω;τ di ) = ⎜
+
2
⎜ 1 + ω 2τ dig
1 + ω 2τ di2 ⎟
⎝
⎠
1
1
1
1 ; 1
1
1
1 ; i = 1,2
=
+
+
=
+ H +
τ dig τ m τ g Tie
τ dig τ m τ
Tie
[23]
[24]
[25]
1
1
1
= + H
H
τ
τg τl
The spectral density functions are given by Eq. [23].
Second sphere 1H relaxation:
r12nd =
1
2nd,H
T1dd
C
2nd,H
dd
1
τ
2nd,H
di
[26]
1
q 2nd
1
1
q 2nd
1
×
× 2nd,H
≅
×
× 2nd,H
2nd
1000 55.55 T1dd + τ m
1000 55.55 T1dd
=C
2nd,O
dd
⎛
2nd,H
3τ d1
⎜
⎜ 1 + ω τ 2nd,H
I d1
⎝
(
)
2
+
2nd,H
7τ d2
(
2nd,H
1 + ωS τ d2
)
[27]
⎞
⎟
2
⎟
⎠
[28]
2
2 2
2
2 ⎛ μ ⎞ h γ 1 H γS
= ⎜ 0⎟
S ( S + 1)
2nd 6
15 ⎝ 4π ⎠ rGdO
(
2nd
= k ex
+
)
[29]
1
1
+
τ H Tie
[30]
1
1
1
= +
τ H τ g τ lH
Outer sphere 1H relaxation:
The outer-sphere contribution can be described by Eq. [31] where NA is the Avogadro constant, and Jos
is its associated spectral density function. 6,7
32 N Aπ
405
2
2 2 2
⎛ μ0 ⎞ = γ S γ I
S ( S + 1) ⎡⎣3J os (ωI ; T1e ) + 7 J os (ωS ; T2 e ) ⎤⎦
⎜
⎟
⎝ 4π ⎠ aGdH DGdH
1/ 2
⎡
1⎛
τ GdH ⎞
⎢
1 + ⎜ iωτ GdH +
⎢
Tje ⎟⎠
4⎝
J os (ω , T je ) = Re ⎢
1/ 2
τ
τ GdH ⎞
4⎛
τ GdH ⎞ 1 ⎛
⎢ ⎛
i
i
1
ωτ
ωτ
+
+
+
+
⎜
⎟
⎜
⎟⎟ + ⎜⎜ iωτ GdH + GdH
GdH
GdH
⎢ ⎜
⎟
⎜
T je
T je ⎠
T je ⎠ 9 ⎝
9⎝
⎣ ⎝
r1os =
[31]
⎤
⎥
⎥ ; j = 1,2
3/ 2 ⎥
⎞ ⎥
⎟⎟ ⎥
⎠ ⎦
[32]
2
aGdH
[33]
DGdH
aGdH is the distance of closes approach and DGdH is the diffusion coefficient for the diffusion of a water
proton relative to the Gd(III) complex.
τ GdH =
4
Electron spin relaxation:
The longitudinal and transverse electronic relaxation rates, 1/T1e and 1/T2e are described by SolomonBloembergen-Morgan theory modified by Powell (Eqs. [34]-[35]), where τV is the correlation time for
the modulation of the zero-field-splitting interaction.
⎛ 1 ⎞
⎜ ⎟
⎝ T1e ⎠
ZFS
⎛ 1 ⎞
⎜
⎟
⎝ T2 e ⎠
=
ZFS
⎛
⎞
1 2
1
4
Δ τ v {4 S ( S + 1) − 3}⎜
+
2 2
2 2 ⎟
25
⎝ 1 + ωSτ v 1 + 4ωSτ v ⎠
⎛
⎞
5.26
7.18
= Δ 2τ v ⎜
+
⎟
2 2
⎝ 1 + 0.372ωSτ v 1 + 1.24ωSτ v ⎠
[34]
[35]
Temperature dependences of water exchange rates and correlation times:
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 kex298 is the exchange rate
at 298.15 K. In Eq. [37] ΔH‡2nd is the enthalpy of activation for the second sphere water exchange
process and kex2nd,298 is the corresponding exchange rate at 298 K.
⎧ ΔS ‡ ΔH ‡ ⎫ kex298T
⎧ ΔH ‡ ⎛ 1
1 k BT
1 ⎞⎫
[36]
=
−
− ⎟⎬
exp ⎨
exp ⎨
kex =
⎬=
⎜
R
298.15
298.15
T
τm
h
RT
R
⎝
⎠
⎭
⎩
⎭
⎩
2 nd ,298
‡2 nd
[37]
⎧ ΔH
k
1 ⎞⎫
⎛ 1
kex2 nd =
ex
298.14
exp ⎨
⎩
T
− ⎟⎬
⎜
⎝ 298.15 T ⎠ ⎭
All correlation times and the diffusion constant are supposed to obey an Arrhenius law:
⎧E 1
1 ⎞⎫
τ = τ 298 exp ⎨ a ⎜⎛ −
⎟⎬
⎩ R ⎝ T 298.15 ⎠ ⎭
1 ⎞⎫
⎧E ⎛ 1
298
DGdH = DGdH
exp ⎨ GdH ⎜
− ⎟⎬
⎩ R ⎝ 298.15 T ⎠ ⎭
5
[38]
[39]
Table S1: Proton relaxivities (r1 / mM-1s-1) of G5-(Gd(DTTAP))63, c(GdIII)=5.3 mM, pH=6.25, at
variable temperature.
ν (1H)/MHz
0.010
0.014
0.021
0.030
0.043
0.062
0.089
0.127
0.183
0.264
0.379
0.546
0.784
1.13
1.62
2.34
3.36
4.83
6.95
10.0
11.5
12.0
13.2
13.6
15.2
15.5
17.4
17.6
20
30
40
60
100
200
5°C
22.6
22.7
22.4
22.4
22. 5
22.5
22.5
22.5
22.4
22.3
22.0
21.8
21.1
20.6
19.9
19.1
18.5
17.9
17.5
21.4
22.8
23.8
25.1
26.0
27.6
26.0
24.7
20.6
14.8
9.10
15°C
23.2
23.4
23.4
23.4
23.4
23.3
23.3
23.3
23.2
23.2
22.8
22.4
21.8
21.3
20.5
19.9
19.0
18.8
19.0
22.2
23.9
24.9
26.4
27.6
28.8
29.4
27.9
22.4
14.8
8.74
25°C
22.5
22.3
22.5
22.4
22.4
22.5
22.5
22.3
22.3
22.2
21.9
21.6
21.0
20.4
19.6
18.8
18.0
17.3
17.2
21.5
23.0
24.7
26.5
28.3
30.4
30.6
28.9
23.0
14.7
8.34
6
37°C
20.2
20.3
20.1
20.2
20.3
20.3
20.1
20.1
20.1
20.1
19.8
19.4
18.8
18.2
17.7
16.7
16.2
15.6
15.5
18.8
20.0
21.6
23.5
25.2
26.8
28.5
27.3
22. 0
14.1
7.83
50°C
18.1
18.1
18.0
18.1
18.1
18.0
18.0
17.9
17.9
17.8
17.5
17.2
16.7
16.2
15.6
15.0
14.4
13.7
13.4
16.4
17.7
18.9
20.3
22.2
23.5
24.1
23.5
19.8
13.2
7.55
Table S2: Proton relaxivities (r1 / mM-1s-1) of [Gd(DTTAP-bz-NH2)(H2O)]2-, c(GdIII)=4.2 mM,
pH=6.75, at variable temperature.
ν (1H)/MHz
0.010
0.014
0.021
0.030
0.043
0.062
0.089
0.127
0.183
0.264
0.379
0.546
0.784
1.13
1.62
2.34
3.36
4.83
6.95
10.0
10.0
11.6
13.4
15.5
18
20
30
40
60
100
200
400
5°C
14.0
14.0
14.0
13.8
13.9
13.9
14.0
14.0
13.9
14.0
13.9
13.5
13.7
13.5
13.2
12.7
12.3
11.6
10.9
11.1
11.0
10.9
10.8
10.8
10.8
10.7
10.6
10.6
10.6
10.3
9.48
7.92
25°C
9.58
9.56
9.63
9.61
9.64
9.61
9.56
9.59
9.59
9.58
9.53
9.56
9.48
9.37
9.27
9.11
8.76
8.27
7.81
7.27
7.08
6.87
6.62
6.44
6.34
6.34
6.22
6.23
6.08
5.88
5.49
7
37°C
8.02
8.07
7.99
7.93
8.15
8.06
8.04
8.05
8.04
8.07
8.11
7.98
7.99
7.85
7.86
7.68
7.49
7.20
6.72
5.97
5.68
5.39
5.20
4.97
5.02
4.75
4.60
4.51
4.43
4.26
4.19
50°C
6.26
6.26
6.30
6.26
6.25
6.22
6.22
6.25
6.22
6.25
6.25
6.18
6.17
6.15
6.07
6.00
5.87
5.64
5.36
4.80
4.55
4.34
4.09
3.93
4.08
3.76
3.61
3.46
3.42
3.32
3.24
Table S3: Proton relaxivities (r1 / mM-1s-1) of [Gd(DTTAP-bz-NO2)(H2O)]2-, c(GdIII)=3.8 mM,
pH=6.59, at variable temperature.
ν (1H)/MHz
0.010
0.014
0.021
0.030
0.043
0.062
0.089
0.127
0.183
0.264
0.379
0.546
0.784
1.13
1.623
2.34
3.36
4.83
6.95
10.0
11.5
13.2
15.2
17.4
20
30
40
60
100
200
400
5°C
14.2
14.2
14.3
14.3
14.2
14.2
14.2
14.2
14.2
14.1
14.1
14.0
13.8
13.6
13.3
12.8
12.4
11.6
11.0
10.9
10.7
10.8
10.6
10.6
10.7
10.2
10.2
10.3
9.90
9.36
8.23
25°C
10.1
10.1
10.1
10.1
10.1
10.1
10.1
10.1
10.1
10.1
10.1
10.1
9.99
9.81
9.67
9.43
9.07
8.58
7.77
7.58
7.27
7.04
6.87
6.72
6.76
6.34
6.27
6.23
6.01
5.84
5.46
8
37°C
8.22
8.24
8.24
8.21
8.22
8.24
8.22
8.21
8.19
8.18
8.20
8.15
8.13
8.04
7.96
7.72
7.48
7.08
6.54
6.07
5.84
5.61
5.34
5.16
5.24
4.74
4.60
4.51
4.45
4.32
4.23
50°C
6.82
6.84
6.81
6.84
6.80
6.81
6.80
6.81
6.79
6.79
6.78
6.74
6.75
6.68
6.59
6.48
6.26
5.94
5.49
5.16
4.93
4.68
4.45
4.31
4.34
3.76
3.61
3.47
3.39
3.32
3.23
Table S4: Variable temperature reduced transverse and longitudinal 17O relaxation rates of G5-(Gd(DTTAP))63, c(GdIII)=39 mM, pH=5.69, Pm=7.95·10-4 at
9.4 T. Reference was G5-(Y(DTTAP))63, c(YIII)=34 mM, pH=5.83.
t / °C
5.4
10.7
18.3
23.6
30.3
40.2
49.2
59.7
70.5
81.3
T/K
278.6
283.9
291.5
296.8
303.5
313.4
322.4
332.9
343.7
354.5
1000/T / K-1
3.59
3.52
3.43
3.37
3.30
3.19
3.10
3.00
2.91
2.82
T1 (Gd)/s
2.41E-03
2.91E-03
3.47E-03
3.93E-03
4.59E-03
5.60E-03
6.73E-03
7.99E-03
9.62E-03
1.17E-02
T1 (Y)/s
2.80E-03
3.39E-03
4.31E-03
5.02E-03
6.11E-03
7.83E-03
9.62E-03
1.19E-02
1.47E-02
1.78E-02
T2(Gd)/s
9.15E-04
8.38E-04
6.80E-04
6.87E-04
7.02E-04
9.25E-04
1.16E-03
1.66E-03
2.49E-03
3.76E-03
T2(Y)/s
2.00E-03
2.47E-03
3.24E-03
3.92E-03
5.00E-03
6.77E-03
8.62E-03
1.10E-02
1.40E-02
1.71E-02
ln(1/T1r)
11.19
11.02
11.16
11.15
11.13
11.07
10.93
10.86
10.72
10.51
ln(1/T2r)
13.52
13.81
14.20
14.23
14.25
13.98
13.75
13.38
12.94
12.47
Table S5: Variable temperature reduced transverse and longitudinal 17O relaxation rates of G5-(Gd(DTTAP))63, c(GdIII)=39 mM, pH=5.69, Pm=7.95·10-4 at
4.7 T. Reference was G5-(Y(DTTAP))63, c(YIII)=34 mM, pH=5.83.
t / °C
6.0
10.3
14.3
18.8
24.1
29.6
37.2
47.9
58.7
71.1
81.8
T/K
279.2
283.5
287.5
292.0
297.3
302.8
310.4
321.1
331.9
344.3
355.0
1000/T / K-1
3.58
3.53
3.48
3.43
3.36
3.30
3.22
3.11
3.01
2.90
2.82
T1 (Gd)/s
2.05E-03
2.31E-03
2.48E-03
2.74E-03
3.15E-03
3.57E-03
4.23E-03
5.27E-03
6.52E-03
8.58E-03
1.09E-02
T1 (Y)/s
2.68E-03
3.14E-03
3.52E-03
4.11E-03
4.88E-03
5.64E-03
6.94E-03
8.86E-03
1.14E-02
1.45E-02
1.74E-02
9
T2(Gd)/s
8.98E-04
9.12E-04
7.81E-04
8.41E-04
8.52E-04
8.47E-04
1.06E-03
1.27E-03
1.81E-03
2.72E-03
3.86E-03
T2(Y)/s
1.93E-03
2.30E-03
2.67E-03
3.13E-03
3.83E-03
4.58E-03
5.90E-03
7.90E-03
1.05E-02
1.35E-02
1.68E-02
ln(1/T1r)
11.89
11.88
11.92
11.94
11.86
11.77
11.66
11.48
11.32
10.99
10.66
ln(1/T2r)
13.53
13.63
13.95
13.91
13.95
14.01
13.78
13.63
13.26
12.82
12.43
Table S6: Variable temperature reduced transverse and longitudinal 17O relaxation rates of [Gd(DTTAP-bz-NH2)(H2O)]2-, c(GdIII)=46 mM, pH=5.51,
Pm=8.19·10-4 at 9.4 T. Reference was acidified H2O, pH=3.3.
t / °C
5.8
12.5
19.6
29.1
39.2
45.9
55.4
59.9
64.5
75.4
85.7
T/K
279.0
285.7
292.8
302.3
312.4
319.1
328.6
333.1
337.7
348.6
358.9
1000/T / K-1
3.58
3.50
3.42
3.31
3.20
3.13
3.04
3.00
2.96
2.87
2.79
T1 (Gd)/s
3.28E-03
4.16E-03
5.15E-03
6.63E-03
8.60E-03
9.95E-03
1.20E-02
1.30E-02
1.40E-02
1.70E-02
1.96E-02
T1 (H2O)/s
3.99E-03
5.02E-03
6.17E-03
7.95E-03
1.02E-02
1.16E-02
1.39E-02
1.51E-02
1.64E-02
1.95E-02
2.25E-02
T2(Gd)/s
7.85E-04
6.68E-04
6.47E-04
7.12E-04
9.70E-04
1.29E-03
1.77E-03
2.14E-03
2.56E-03
4.10E-03
5.92E-03
T2(H2O)/s
4.02E-03
5.00E-03
6.26E-03
7.95E-03
1.03E-02
1.16E-02
1.39E-02
1.50E-02
1.63E-02
1.94E-02
2.25E-02
ln(1/T1r)
11.09
10.82
10.58
10.33
9.99
9.76
9.58
9.49
9.47
9.12
8.99
ln(1/T2r)
14.04
14.27
14.34
14.26
13.95
13.65
13.31
13.10
12.90
12.37
11.93
Table S7: Variable temperature reduced transverse and longitudinal 17O relaxation rates of [Gd(DTTAP-bz-NO2)(H2O)]2-, c(GdIII)=32 mM, pH=5.91,
Pm=5.73·10-4 at 9.4 T. Reference was acidified H2O, pH=3.3.
t / °C
5.8
12.5
19.6
29.1
39.2
45.9
55.4
59.9
64.5
75.4
85.7
T/K
279.0
285.7
292.8
302.3
312.4
319.1
328.6
333.1
337.7
348.6
358.9
1000/T / K-1
3.58
3.50
3.42
3.31
3.20
3.13
3.04
3.00
2.96
2.87
2.79
T1 (Gd)/s
3.43E-03
4.39E-03
5.39E-03
6.93E-03
8.95E-03
1.02E-02
1.24E-02
1.35E-02
1.46E-02
1.75E-02
2.04E-02
T1 (H2O)/s
3.99E-03
5.02E-03
6.17E-03
7.95E-03
1.02E-02
1.16E-02
1.39E-02
1.51E-02
1.64E-02
1.95E-02
2.25E-02
10
T2(Gd)/s
1.07E-03
9.24E-04
8.37E-04
9.13E-04
1.20E-03
1.50E-03
2.09E-03
2.45E-03
3.02E-03
4.63E-03
6.66E-03
T2(H2O)/s
4.02E-03
5.00E-03
6.26E-03
7.95E-03
1.03E-02
1.16E-02
1.39E-02
1.50E-02
1.63E-02
1.94E-02
2.25E-02
ln(1/T1r)
11.16
10.81
10.63
10.38
10.05
9.93
9.63
9.53
9.47
9.20
9.01
ln(1/T2r)
13.99
14.25
14.41
14.34
14.07
13.83
13.47
13.30
13.06
12.57
12.13
Table S8. Calculation of the number of chelating groups per dendrimer.
G5-(Gd(DTTAP))63
n = number of mols of chelate per gram of product
9.89×10-4
obtained from complexometric titration
Total percentage of C obtained from
48.9
elemental analysis
Percentage of carbon in the chelate
24.9
(DTTAP-bz-NCS = C21H29N4O10S) calculated from n
Percentage of carbon in PAMAM skeleton
48.9-24.9 = 24.0
G5-(NH2)128
Formula of PAMAM skeleton
C1262H2528N506O252
x = number of chelate bound on the dendrimer
63
Percentage of substituted amino groups
49%
Total percentage of N calculated by using x
16.6
Total percentage of N obtained by
17.3
elemental analysis
Total percentage of S calculated by using x
3.1
Total percentage of S obtained by
2.8
elemental analysis
Total percentage of P calculated by using x
3.0
Total percentage of P obtained by
2.7
elemental analysis
Figure S1. Variable temperature reduced 17O chemical shifts of [Gd(DTTAP-bz-NO2)(H2O)]2-,
c(GdIII)=32 mM, pH=5.91, Pm=5.73·10-4 at 9.4 T. Reference was acidified H2O, pH=3.3.
5
2x10
5
1x10
0
5
-1x10
5
ωr / rad s
-1
-2x10
5
-3x10
5
-4x10
5
-5x10
5
-6x10
5
-7x10
-8x10
5
2.8
3.0
3.2
3.4
-1
1000/T / K
11
3.6
Figure S2. Variable temperature reduced 17O chemical shifts of [Gd(DTTAP-bz-NH2)(H2O)]2-,
c(GdIII)=46 mM, pH=5.51, Pm=8.19·10-4 at 9.4 T. Reference was acidified H2O, pH=3.3.
5
2x10
5
1x10
0
5
-1x10
5
ωr / rad s
-1
-2x10
5
-3x10
5
-4x10
5
-5x10
5
-6x10
5
-7x10
5
-8x10
2.8
3.0
3.2
3.4
3.6
-1
1000/T / K
Figure S3. Variable temperature reduced 17O chemical shifts of G5-(Gd(DTTAP))63, c(GdIII)=39 mM,
pH=5.69, Pm=7.95·10-4 at 4.7 T (○) and 9.4 T (▲). Reference was G5-(Y(DTTAP))63, c(YIII)=34 mM,
pH=5.83.
5
2x10
5
1x10
0
ωr / rad s
-1
5
-1x10
5
-2x10
5
-3x10
5
-4x10
5
-5x10
5
-6x10
2.8
2.9
3.0
3.1
3.2
3.3
-1
1000/T / K
12
3.4
3.5
3.6
3.7
Table S9. Fitted parameters of G5-(Gd(DTTAP))63. The underlined parameters were fixed during the
fitting.
Parameter
G5-(Gd(DTTAP))63
298
6 -1
kex [10 s ]
5.0±0.2
‡
-1
56.2±1.0
ΔH [kJ mol ]
+71.9±3
ΔS‡ [J mol-1K-1]
6
-1
-3.8
A/ħ [10 rad s ]
298
4417±340
τgO [ps]
21±2
ΕgO [kJ mol-1]
298
71±3
τlO [ps]
21±2
ΕlO [kJ mol-1]
2
0.28±0.01
S
298
21±2
τV [ps]
5.5±5.4
ΕV [kJ mol-1]
0.62±0.11
Δ2[1020 s-2]
1.7±0.1
δgL2 [10-2]
rGdO [Å]
2.5
rGdHouter [Å]
3.5
7.58
χ(1+η2/3)1/2 [MHz]
q
1
q2nd
2
298
50
τM 2nd [ps]
‡
-1
35.0
ΔH 2nd [kJ mol ]
r2ndGdH [Å]
3.5
2nd
r GdO [Å]
4.1
13
Table S10. Fitted parameters of [Gd(DTTAP-bz-NO2)(H2O)]2- and [Gd(DTTAP-bz-NH2)(H2O)]2-.
The underlined parameters were fixed during the fitting.
Parameter
kex298 [106 s-1]
ΔH‡ [kJ mol-1]
ΔS‡ [J mol-1K-1]
A/ħ [106 rad s-1]
τRO298 [ps]
ΕR [kJ mol-1]
τV298 [ps]
ΕV [kJ mol-1]
Δ2[1020 s-2]
298
D GdH [10-10m2s-1]
ΕDGdH [kJ mol-1]
δgL2 [10-2]
τRH298/ τRO298
rGdO [Å]
rGdH [Å]
rGdHouter [Å]
χ(1+η2/3)1/2 [MHz]
q
q2nd
τM2982nd [ps]
ΔH‡2nd [kJ mol-1]
r2ndGdH [Å]
r2ndGdO [Å]
[Gd(DTTAP-bz-NH2)(H2O)]28.9±1.3
48.1±3
+49.8±10
-3.8
116±2
20.5±0.8
28.2±0.5
1
0.403±0.003
25±2
30±1
3.3±0.6
0.81±0.04
2.5
3.1
3.5
7.58
1
2
50
35.0
3.5
4.1
[Gd(DTTAP-bz-NO2)(H2O)]28.3±0.6
48.5±2
+50.3±8
-3.8
117±10
18±1
26.3±0.4
1
0.40±0.01
25±2
30±1
2.8±0.5
0.85±0.08
2.5
3.1
3.5
7.58
1
2
50
35.0
3.5
4.1
References for equations.
1
T. J. Swift, R. E. Connick, J. Chem. Phys., 1962, 37, 307.
J. R. Zimmermann, W. E. Brittin, J. Phys. Chem., 1957, 61, 1328.
3
G. Lipari, S. Szabó, J. Am. Chem. Soc., 1982, 104, 4546.
4
G. Lipari, S. Szabó, J. Am. Chem. Soc., 1982, 104, 4559.
5
Z. Luz, S. Meiboom, J. Chem. Phys., 1964, 40, 2686.
6
J. H. Freed, J. Chem. Phys., 1978, 68, 4034.
7
S. H. Koenig, R. D. Brown III, Prog. Nucl. Magn. Reson. Spectrosc., 1991, 22, 487.
2
14