Research article Received: 26 February 2015
Revised: 16 July 2015
Accepted: 23 July 2015
Published online in Wiley Online Library: 25 August 2015
(wileyonlinelibrary.com) DOI 10.1002/mrc.4320
Refinement of the inversion-transfer NMR experiment for faster characterization of chemical exchange Evelyne Baguet* It is shown theoretically that the inversion-transfer experiment used to estimate the value of unidirectional rate constants in chemical exchange systems can be performed faster via a reduction of the recovery delay. The chemical exchange rate constants can then be estimated accurately with a formula close to that of standard inversion transfer and easy to use, after a justified approximation. A function was developed to determine the optimal value of the recovery delay for an optimal inversion-transfer sequence. The validity of these theoretical results was checked experimentally with a solution of N,N-dimethylacetamide in which chemical exchange arises from internal hindered rotation. Copyright © 2015 John Wiley & Sons, Ltd. Keywords: chemical exchange; inversion transfer; magnetization transfer; high resolution NMR
Introduction
Magn. Reson. Chem. 2016, 54, 51–57
Theory Chemical exchange in a two-spin system We consider a sample where the nuclei, of magnetogyric ratio , occupy alternatively two different chemical sites. At any time, the sample is composed of two populations A and B, giving rise to two different resonances. It is assumed that there is no chemical exchange nor dipolar interactions of A and B with other nuclei. The chemical exchange process, which is a transfer of matter, is coupled to an exchange of magnetization. As these two exchange phenomena have the same origin, they are characterized by the same unidirectional rate constants kA and kB of interconversion
*Correspondence to: Evelyne Baguet, CEISAM CNRS UMR 6230, Département de Chimie, Université de Nantes, 2 rue de la Houssiniére, F-44322 Nantes cedex 3, France. E-mail: [email protected] CEISAM CNRS UMR 6230, Département de Chimie, Université de Nantes, 2 rue de la Houssiniére, F-44322 Nantes cedex 3, France
Copyright © 2015 John Wiley & Sons, Ltd.
51
NMR magnetization-transfer methods [1,2] enable the study of chemical exchange and cross-relaxation between nuclear spins. They are among the many NMR methods used in chemistry to study the structure and dynamics of molecules.[3,4] In biological systems, they are employed for the direct characterization of enzymatic reactions and transport properties in living cells.[5–7] They are also employed as contrast agents in magnetic resonance imaging with the chemical exchange saturation-transfer method.[8,9] Among these methods, inversion transfer has been developed by Dahlquist et al. [10] for symmetrical chemical exchange systems and generalized two years later by Alger, Prestegard,[11] Brown and Ogawa.[12] It consists, for a chemical exchange system at equilibrium in a static magnetic field B0 , in selectively inverting one of the exchanging magnetizations, when studying the time course of all magnetization in chemical exchange. It can be useful when one wants to study unidirectional rates of complex chemical reactions in various systems [13–17] without the spill-over effect, which can occur in saturation-transfer experiments.[18] Recently, in the magnetic resonance imaging domain, the use of a selective magnetization inversion in the presence of chemical exchange helped to understand better the changes in the macromolecular contents of tumors and interpret imaging contrasts.[19] Also, a new method of chemical exchange study, called exchange kinetics by inversion transfer (EKIT) and using the inversion-transfer principle, has been developed to study simultaneous reactions.[20] In this work, a selective inversion pulse was applied successively at different frequencies to give a map. The determination of chemical exchange via the inversiontransfer sequence has been estimated precisely by Led and Gesmar.[21] Whereas the efficiency of the saturation-transfer experiment has been improved in the past,[22] it seems that no similar optimisation of the inversion-transfer sequence has
been performed. However, this could be very interesting, as the inversion-transfer method may be useful but is very time consuming, particularly for systems with long longitudinal relaxation times. Also, a precise study of magnetization time-course after a selective inversion could be useful for new experiments using selective inversion in the presence of chemical exchange. We propose here to improve the inversion-transfer sequence so that the recycling delay may be significantly reduced while the values of unidirectional chemical exchange rate constants can still be reliably estimated. For a given inversion-transfer experiment, we define a function called ‘efficiency’ proportional to the signal to noise ratio and the temporary decrease of the non-inverted peak. The maximal value of this efficiency function gives the optimal recovery delay to evaluate accurately the value of the chemical exchange rate in a minimum experimental time.
E. Baguet between populations A and B. They are usually represented by the scheme kA
A•B kB
This dynamic process can also be characterized by the time constants A D 1=kA and B D 1=kB . The magnetization values of the two populations A and B at thermodynamic equilibrium are MA0 and MB0 , respectively; their resonance frequencies are called A and B . If T1A and T1B are the relaxation times of A and B in the absence of exchange, it is expedient to define the time constants 1A and 1B : 1 1 1 D C 1A T1A A
1 1 1 D C 1B T1B B
and
(1)
The dynamic properties of the exchanging system are described by the Bloch equations modified for chemical exchange [23] and give, along the z axis, 8
> 0 B A
Eqn 13 can be modified this way:
1=1B 1=1A 1=1B 1=1A D q
Revised: 16 July 2015
Accepted: 23 July 2015
Published online in Wiley Online Library: 25 August 2015
(wileyonlinelibrary.com) DOI 10.1002/mrc.4320
Refinement of the inversion-transfer NMR experiment for faster characterization of chemical exchange Evelyne Baguet* It is shown theoretically that the inversion-transfer experiment used to estimate the value of unidirectional rate constants in chemical exchange systems can be performed faster via a reduction of the recovery delay. The chemical exchange rate constants can then be estimated accurately with a formula close to that of standard inversion transfer and easy to use, after a justified approximation. A function was developed to determine the optimal value of the recovery delay for an optimal inversion-transfer sequence. The validity of these theoretical results was checked experimentally with a solution of N,N-dimethylacetamide in which chemical exchange arises from internal hindered rotation. Copyright © 2015 John Wiley & Sons, Ltd. Keywords: chemical exchange; inversion transfer; magnetization transfer; high resolution NMR
Introduction
Magn. Reson. Chem. 2016, 54, 51–57
Theory Chemical exchange in a two-spin system We consider a sample where the nuclei, of magnetogyric ratio , occupy alternatively two different chemical sites. At any time, the sample is composed of two populations A and B, giving rise to two different resonances. It is assumed that there is no chemical exchange nor dipolar interactions of A and B with other nuclei. The chemical exchange process, which is a transfer of matter, is coupled to an exchange of magnetization. As these two exchange phenomena have the same origin, they are characterized by the same unidirectional rate constants kA and kB of interconversion
*Correspondence to: Evelyne Baguet, CEISAM CNRS UMR 6230, Département de Chimie, Université de Nantes, 2 rue de la Houssiniére, F-44322 Nantes cedex 3, France. E-mail: [email protected] CEISAM CNRS UMR 6230, Département de Chimie, Université de Nantes, 2 rue de la Houssiniére, F-44322 Nantes cedex 3, France
Copyright © 2015 John Wiley & Sons, Ltd.
51
NMR magnetization-transfer methods [1,2] enable the study of chemical exchange and cross-relaxation between nuclear spins. They are among the many NMR methods used in chemistry to study the structure and dynamics of molecules.[3,4] In biological systems, they are employed for the direct characterization of enzymatic reactions and transport properties in living cells.[5–7] They are also employed as contrast agents in magnetic resonance imaging with the chemical exchange saturation-transfer method.[8,9] Among these methods, inversion transfer has been developed by Dahlquist et al. [10] for symmetrical chemical exchange systems and generalized two years later by Alger, Prestegard,[11] Brown and Ogawa.[12] It consists, for a chemical exchange system at equilibrium in a static magnetic field B0 , in selectively inverting one of the exchanging magnetizations, when studying the time course of all magnetization in chemical exchange. It can be useful when one wants to study unidirectional rates of complex chemical reactions in various systems [13–17] without the spill-over effect, which can occur in saturation-transfer experiments.[18] Recently, in the magnetic resonance imaging domain, the use of a selective magnetization inversion in the presence of chemical exchange helped to understand better the changes in the macromolecular contents of tumors and interpret imaging contrasts.[19] Also, a new method of chemical exchange study, called exchange kinetics by inversion transfer (EKIT) and using the inversion-transfer principle, has been developed to study simultaneous reactions.[20] In this work, a selective inversion pulse was applied successively at different frequencies to give a map. The determination of chemical exchange via the inversiontransfer sequence has been estimated precisely by Led and Gesmar.[21] Whereas the efficiency of the saturation-transfer experiment has been improved in the past,[22] it seems that no similar optimisation of the inversion-transfer sequence has
been performed. However, this could be very interesting, as the inversion-transfer method may be useful but is very time consuming, particularly for systems with long longitudinal relaxation times. Also, a precise study of magnetization time-course after a selective inversion could be useful for new experiments using selective inversion in the presence of chemical exchange. We propose here to improve the inversion-transfer sequence so that the recycling delay may be significantly reduced while the values of unidirectional chemical exchange rate constants can still be reliably estimated. For a given inversion-transfer experiment, we define a function called ‘efficiency’ proportional to the signal to noise ratio and the temporary decrease of the non-inverted peak. The maximal value of this efficiency function gives the optimal recovery delay to evaluate accurately the value of the chemical exchange rate in a minimum experimental time.
E. Baguet between populations A and B. They are usually represented by the scheme kA
A•B kB
This dynamic process can also be characterized by the time constants A D 1=kA and B D 1=kB . The magnetization values of the two populations A and B at thermodynamic equilibrium are MA0 and MB0 , respectively; their resonance frequencies are called A and B . If T1A and T1B are the relaxation times of A and B in the absence of exchange, it is expedient to define the time constants 1A and 1B : 1 1 1 D C 1A T1A A
1 1 1 D C 1B T1B B
and
(1)
The dynamic properties of the exchanging system are described by the Bloch equations modified for chemical exchange [23] and give, along the z axis, 8
> 0 B A
Eqn 13 can be modified this way:
1=1B 1=1A 1=1B 1=1A D q
