Relaxivity: definitions

Transcription

1 EMMI Intensive Programme "Design, Synthesis and Validation of Imaging Probes" orino, September 9-3, Gd(III) complexes: basic relaxometric characterization Eliana Gianolio Relaxivity: definitions Diamagnetic contribution R iobs = [CA]r ip + R iw i =, Observed Relaxation Rate relaxivity r p [s - mm - ] Contribution to the observed water proton relaxation rate that a paramagnetic complex gives to a solution in which it is solved in mm concentration R obs (s - ) 4 r p = 8.6 mm - s OOC -OOC -OOC N N Gd 3+ N O N H B956 -OOC -OOC Gd 3+ r p = 4,7 mm - s - -,,5,,5,,5 H OH [CA] mm COO- COO- COO- COO- N N N COO- COO- It is function of many parameters B,, ph, q, τ R, τ M, r, e,

2 Check the absence of free Gd(III) ion by Xylenol Orange spectrophotometric method 7 µl of the Gd-L solution + 7 µl of Xylenol Orange solution (3 mg/ 5 ml Acetic buffer) Free dye Gd-bound dye A. Barge et al. CONRAS MEDIA & MOLECULAR IMAGING : (6) How to determine the concentration of a paramagnetic complex -ICP-MS -Relaxometric Procedure: he procedure consists of: r ip =(R iobs - R iw )/[CA] ) mineralizing the complex solution at very acidic ph, at high temperature for 4h in order to cause the release of all the metal ion from the complex µl GdL solution + µl Concentrated strong acid (HCl 37% or HNO 3 5M) Acidic Acidic solution solution C, overnight in a sealed glass vial ) Measuring the observed H-longitudinal relaxation rate of the acidic solution: R obs = [Gd]r p + R dia In acidic conditions, at MHz and 98K: R dia =.5 r p (Gd-aquoion)= 3.5 mm - s - [Gd(III)] = R obs [GdL] = [Gd(III)]

3 How to determine the concentration of a paramagnetic complex -Lanthanide ion induced paramagnetic shift (Evans Method): Complex solution + % terbutoh δ D O + % terbutoh δ = d + c + p + χ Diamagnetic contribution Contact contribution Pseudocontact contribution BMS (Bulk Magnetic Susceptibility) contribution C = molar concentration S = /3 for vertical magnets /6 for horizontal magnets = emperature in Kelvin χ = 4πCS (K) µeff = effective magnetic moment (for Gd(III) = 7.94) µeff.84 echniques for a basic relaxometric characterization of Gd-L - H-water longitudinal relaxation rate at a fixed field as a function of: emperature ph Concentration of an interacting substrate time... - Magnetic field dependence of H-water longitudinal relaxation rate (NMRD Profiles) τ R Informations about q Electronic relaxation time - emperature dependence of the 7 O-water transverse relaxation rate τ M Informations about q Electronic relaxation time

4 - H-water longitudinal relaxation rate at a fixed field (/R ) measurement through the Inversion Recovery sequence 8 τ 9 Acquisition Proton Relaxation Enhancement (PRE) Method Exploits the water protons relaxation enhancement induced by the interaction of a low molecular weight Gd-complex with a macromolecular substrate Gd + M Gd M Low Relaxivity R obs High Relaxivity R obs * Relaxation Enhancement ε = R obs *- R M R obs - R w

5 Proton Relaxation Enhancement (PRE) Method Informations about K a (Association Constant) R b (Relaxivity of the adduct) n (Number of independent binding sites) K A = [ Gd L / M ] [ Gd L][ nm ] Gd-L + M Gd-L/M R obs = r [GdL] + r b [GdL-M] + R d R obs ( r b ( K = r + r A [ Gd L] + nk [ M ] + ) ( K [ Gd L] + nk [ M ] + ) 4K [ Gd L] n[ M ] [ Gd L] ) + R H A A K Main limitation: the concentration of the species involved in the binding equilibrium can not be determined directly the analysis is more difficult in the case of multi-site binding A A A Proton Relaxation Enhancement (PRE) Method he experimental procedure consists of carrying out two distinct titrations Robs (s - ),,8,6,4,,,8 E-titration Gd- Gd- Gd-3 R obs (s - ) M-titration [M] =.5 mm n=3 n= n=,6,,,,3,4,5,6 Substrate (M),,,4,6,8, Gd-L (M) Accurate estimation of the relaxivity of the macromolecular adduct (R b ) and of nk a Accurate independent evaluation of n and K a

6 NMRD Profiles Magnetic field dependence of H-water longitudinal relaxation rate r p (mm - s - ) τ R = 9 ns.4 ns.3 ns,, Proton Larmor Frequency (MHz) r = r + r + r γ IS OS SS p p p p r IS p [ CA] q = 55.6 g S( S + ) β M +τ M 3τ C + ω Hτ C 7τ = H C M 5 rh ω Sτ C τ Ci = τ R + τ M + ie NMRD profiles How to measure at different magnetic field strengths? - single NMR spectrometers operating at different fields (few data points, time (and money) consuming, difficulty to explore low magnetic fields) - single NMR spectrometer tunable at different fields (better but still few data points at low fields and time-consuming) - dedicated NMR spectrometer ( infinite data points, very fast and automated acquisition) Field Cycling Relaxometer

7 Field Cycling Relaxometer NMRD profiles Many NMR pioneers contributed significantly to the development of field-cycling NMR, including Purcell, Slichter, Hahn, Abragam, Redfield, and more recently Noack and Koenig. FFC- relaxometer by Stelar Advantages: -he use of low-inductance magnets allows the field to be switched very rapidly (in milliseconds) to any desirable value (currently in the.- MHz range), maintaining the field stability and homogeneity required for the measurement. - High sensitivity even at very low fields - Only one acquisition field only one transmitter/receiver system NMRD profiles How to measure in the Field Cycling Relaxometer? he equilibrium magnetization of a sample is directly dependent on the magnetic field When the field is switched up or down M changes accordingly with an exponential time dependence, whose time constant corresponds to the value at the final field Field A C B= C t M at field C at field C at field C

8 NMRD profiles How to measure by using the Field Cycling Relaxometer? - For fields lower than 8 MHz: Pre-polarised sequence (Usually 6.78 MHz) he signal is acquired as FID or echo (single or multi) NMRD profiles How to measure by using the Field Cycling Relaxometer? - For fields higher than 8 MHz: Non-polarised sequence

9 NMRD profiles o improve the data analysis, the values acquired with the Field Cycling Relaxometer can be implemented with data measured at any other magnetic field by means of conventional or tunable magnets r p (mm - s - ) ypical NMRD profile from our lab FFC unable magnet (-8 MHz) HR spectrometers ( MHz),, Proton Larmor Frequency (MHz) FFC - mm NMR tube - min. sample volume ca. 5 µl - acquisition time ( data points) ca. 5 - min. R measurable.8 s - unable magnet - 5 mm NMR tube - min. sample volume ca. 5 µl - acquisition time ca. 5 for each field High Resolution spectrometers - 5 mm NMR tube - min. sample volume ca. 5 µl (use of coaxial capillaries for avoiding radiation dumping effects) - acquisition time ca. for each field (including locking and shimming) emperature dependence of the 7 O-water transverse relaxation rate - It is the technique of election for determining the exchange rate of metal bound water molecules in Gd(III) complexes - It is also very sensitive to the hydration state (q) of the metal ion Swift-Connick Equations R R + k R + ω O O O O O O M ex M M p = PM kex O O O M + ex + ωm ( R k ) q PM = 55.6 [ GdL] ω MO = 7 O chemical shift difference between coordinated and bulk water molecule dip quad R = R + R + R + R O O sc O O O Cur M M M M M ransverse relaxation rate of the coordinated water oxygen O sc A τ E RM = S( S + ) τe + 3 h + ωsτe τ = τ + O Ei M ie Most of the parameter determining R po are exactly identical to those that control the proton relaxivity Almost all the relevant parameters are temperature dependent (τ M, τ R, τ V, ω)

10 emperature dependence of the 7 O-water transverse relaxation rate - he temperature dependence of the correlation times may be expressed in terms of Arrhenius or Eyring laws Ej 98 R 98.5 j j e τ = τ τ ( τ ) Sj Hj 98,5 H j kb R R j R 98.5 j = e = e h 98.5 Arrhenius-type dependence Eyring-type dependence - he temperature dependence of the resonance frequency difference between free and metal bound 7 O-water has a different behaviour: ω = O M ( + ) geµ BS S B A 3 k h B emperature dependence of the 7 O-water transverse relaxation rate ransverse relaxation time,, and its measurement is the time-constant of the magnetization decay in the x-y plane after a perturbation pulse 9 (x) pulse he spin-dephasing in the x-y plane is caused by relaxation mechanisms plus magnetic field inhomogeneity = + * inh - can be measured by multi-echo pulse sequence (e.g. CPMG) - * can be simply measured by determining the linewidth at half height of the NMR signal of interest

11 emperature dependence of the 7 O-water transverse relaxation rate When values are extremely short (ms range), as in the case of 7 O-water in an aqueous solution of a Gd(III) complex, the CPMG sequence does not give accurate results. In this case, * is measured, and, upon good shimming conditions, = *. PARAMAGNEIC SYSEMS = π υ * = R = / (in Hz) ω p free bound ν / emperature dependence of the 7 O-water transverse relaxation rate Qualitatively, the shape and the efficacy (normalized to the Gd(III) content) of the paramagnetic contribution of water 7 O-R p values provides an indication about k ex and q. 7O-R p - s B =. Fast exchange Slow exchange emperature - K 7O-R p - s (Gd-DO3A)(H O) k ex x 7 s - (Gd-DOA)(H O) - k ex 5x 6 s - q = q = emperature - K Intermediate exchange

12 emperature dependence of the 7 O-water transverse relaxation rate Some practical info - High resolution NMR spectrometer are used and particular attention has to be paid for maximizing the field homogeneity (improve shimming for reducing R inh ); in addition, deuterated solvents (for field locking) not containing oxygen are preferable. - he sample should be enriched in the water 7 O isotope. An enrichment of ca.. % in the sample under observation is enough for acquiring the entire profile in reasonable times. - he minimum concentration of Gd(III) complex in the sample depends on many factors, among them magnetic field strength, k ex and q values are the most relevant. he concentration should be sufficient to detect a significant paramagnetic contribution. Usually, concentrations around mm are optimal for any conditions. NMRD and 7 O-R p parameters hydration numer q reorientational correlation time τ R exchange lifetime τ M Gd-H w distance r Gd-Ow distance r electronic relaxation times ( ; τ V ) a and D (outer sphere) he reliability of a multi-parameter fitting is sensibly improved if the highest number of parameter as possible is determined by independent measurements

13 the hydration number q luminescence lifetime: b(iii) and Eu(III) complexes luminescence is better quenched in H O than in D O because of a better energy transfer to the OH vibrational streching than to the OD ones. he difference in the luminescence lifetimes in the two solvents is proportional to the hydration number. Horroks and Sudnik q ( ) A = 4. ms = A k H O k - for b(iii) DO.5 ms - for Eu(III) Parker et al. Correction which allows for the contribution of other exchangeable X-H oscillators (N-H and C-H) and of the unbound water molecules q. [ ( k k ). 5] qb = 5[ ( k H ). 6] O k DO Eu = H O D O the hydration number q Dy-induced 7 O shift : for the Dy(III) cation the hyperfine shift is largely dominated by the contact term; the contact 7 O shifts of the bound water molecules do not depend on the structure of the complex and thus they are directly proportional to the hydration number. he method consists in measurement of the 7 O shift of the water signal as a function of the concentration of the paramagnetic complex. A straight line is obtained whose slope is proportional to the q value of the Dy(III) complex. he actual value is then obtained by comparison with the slope of the line obtained with a reference sample, normally the aquoion [Dy(H O) 8 ] d.i.s. (ppm) 4 3 [Dy(H O) 8 ] 3+ Dy-AAZA [DyL] mm d.i.s. = (q /[ /[H O]) ]) ([Dy-L(H O) q ]) q = inner sphere water molecules = 7 O shift of the water signal q /[HO]= slope of the line Slope(Dy(H O) 8 ): 8 = Slope(Dy-L):q

14 Data Analysis ) Only the paramagnetic contribution to the observed NMRD and 7 O-R p vs. profiles must be analyzed. H-NMRD Rp = Robs R d 7 O-R p R = R R O O O p obs d - An accurate determination of the diamagnetic contribution is very important, especially when the concentration of the paramagnetic complex is low. - In principle, the diamagnetic terms should be measured in a solution containing a diamagnetic Ln(III) complex (e.g. La(III), Lu(III) or Y(III)). In practice, it is sufficient to investigate the behaviour of the solution without the Gd(III) complex. - herefore, in a simple aqueous solution of a Gd(III) complex, the diamagnetic term is measured on pure water. he contribution to the NMRD profile is rather small (ca..4 s- at 5 C at any field), whereas for water 7 O-R is rather large ( 7 O is a quadrupolar nucleous) but again field independent 7O-R d - s O-R d emperature - K Data Analysis ) In order to compare profiles (NMRD and 7 O-R p ) measured in different conditions, it is convenient to normalize the paramagentic contribution to a given Gd(III) concentration, e.g mm for NMRD profiles (in this condition R p correspond to the relaxivity of the complex). he normalization is simply done dividing the R ip values by the reference concentration. 3) hen, a proper fitting model for the sample to be analyzed has to be selected: - for NMRD profiles the following models may be considered: - classical inner sphere + outer sphere (total number of parameters = 8) - classical inner sphere + outer sphere + second sphere (treated as modified inner sphere) (number of parameters ) - Lipari-Szabo inner sphere (used when the complex experiences a fast and a slow tumbling motion) + outer sphere (number of parameters = ) - Lipari-Szabo inner sphere + outer sphere + second sphere (number of parameters 3) - for 7 O-R p vs. profiles the total number of parameters involved is.

15 Data Analysis 4) Since most of the parameters controlling H-NMRD and water 7 O-R p vs. profiles are the same, two fitting strategies can be adopted: - each dataset (NMRD and 7 O-R p vs. ) is fitted independently and the obtained results are compared and successively averaged. - all datasets (eventually including NMRD acquired at different temperatures and/or 7 O-R p vs. profiles acquired at different fields) are analysed simultaneously leading to a unique set of fitted parameters. In the former approach each dataset is fitted as better as possible, whereas in the simultaneous approach the fitting quality of all the datasets are invariantly worse.