Slow diffusion and flow of molecules measured by pulsed...

Details Slow diffusion and flow of molecules measured by pulsed... Slow diffusion and flow of molecules measured by pulsed...

2003-05-12

2004-09-21

Shrivastav, Brij B. (Department: 2859)

Electricity: measuring and testing

Particle precession resonance

Using a nuclear resonance spectrometer system

C324S309000

Reexamination Certificate

active

06794866

ABSTRACT:

This application claims Paris Convention priority of EP 02 011 929.3 filed May 29, 2002 the complete disclosure of which is hereby incorporated by reference.
BACKROUND OF THE INVENTION
The invention concerns a pulsed gradient NMR (=nuclear magnetic resonance) method using stimulated echoes for determining the translational isotropic or anisotropic diffusion coefficient of a molecule or supra-molecular assembly or the flow rate and direction of fluids containing such molecules.
A pulsed field gradient NMR method using stimulated echoes is known from A. S. Altieri, D. P. Hinton and R. A. Byrd, J. Am. Chem. Soc. 117 (1985), p. 7566-7567.
In order to determine the translational diffusion coefficient or the flow rate of a macromolecule pulsed field gradient NMR using stimulated echoes can be applied. With suitable hydrodynamic models, it is then possible to estimate the radius and the mass of the macromolecule.
However, slow diffusion coefficients D<10
−10
m
2
/s or small flow rates, which are typically associated with biological macromolecules or supra-molecular assemblies with masses M≧50 kDa, are difficult to measure with this method.
This is due to the rapid longitudinal relaxation of the protons in state of the art measurements.
In methods employing stimulated echoes (STEs), the information about the localization of the molecules is temporarily stored in the form of longitudinal magnetization during a diffusion interval (i.e. a diffusion time) &Lgr;. Usually, the magnetization of protons is used for these experiments, since protons have a favorable gyromagnetic ratio and, of course, protons are present in effectively all macromolecules and biological materials.
However, if during the time of longitudinal relaxation of protons T1(H) no significant diffusion or flow takes place, no determination of the translational diffusion constant or the flow rate can be done. This means materials with short T1(H) values, as compared with the times necessary for significant translational diffusion or flow, are excluded from the above mentioned measurement methods of the state of the art.
One of the principal hurdles that must be overcome prior to the determination of the structures of amphiphilic membrane proteins by solution-state NMR is the optimization of the solubilization of these proteins by suitable lipids, detergents or amphiphilic polymers (“amphipols”). Ideally, the hydrophobic surface of the protein should be covered with the slightest possible layer of solubilizing agent, so that the overall mass of the resulting assembly remains as small as possible. If the overall mass is much larger than that of the protein itself, this translates into slow rotational diffusion, long tumbling correlation times &tgr;
c
, broad NMR lines, and hence poor resolution and sensitivity.
There are several approaches to the determination of the size of a supra-molecular assembly comprising a protein and its associated solubilizing agents: the kinetics of sedimentation during ultra-centrifugation, diffusion through membranes with well-defined pores, chromatography with suitable molecular sieves, neutron diffraction and pulsed-field gradient NMR. The latter method can provide a measurement of the translational diffusion coefficient D. With suitable hydrodynamic models, it is then possible to estimate the radius and hence the mass of macromolecular assemblies. Slow diffusion coefficients D<10
−10
m
2
s
−1
associated with biological macromolecules or supra-molecular assemblies with masses M≧50 kDa are difficult to measure by standard pulsed-field gradient NMR methods (1-5) using stimulated echoes because of rapid longitudinal relaxation of the nuclei (usually protons) that carry the information about the localization of the molecules during the diffusion interval.
The success of the original pulsed field gradient spin-echo NMR method due to Stejskal and Tanner (1) has lead to the development of many variants, particularly methods that employ so-called stimulated echoes (STE's) where the information about the localization of the molecules is temporarily stored in the form of longitudinal magnetization (2). Such experiments are usually carried out using the magnetization of protons, because of the favorable gyromagnetic ratio that allows one to ‘encode’ the initial spatial position with good accuracy without resorting to very intense gradients. Byrd and co-workers (6) have adapted a method (5) with an additional interval where the information is stored in the form of longitudinal proton magnetization to allow eddy currents to die out. More recent experiments allow one to circumvent undesirable effects of eddy currents by using so-called ‘bipolar gradients’ (3). It has also been shown recently that diffusion can be distinguished from flow or convection (4). The development of novel experimental methods has been accompanied by substantial efforts to extract reliable information from the attenuation of the signals as a function of the amplitude of the gradients, which should ideally obey a Gaussian function. The rates of these decays can be estimated by various approaches using inverse Laplace transformations. This has lead to so-called DOSY (Diffusion Ordered Spectroscopy) representations (5), i.e. two-dimensional plots where the diffusion coefficients appear along the ordinates while the chemical shifts are responsible for the dispersion along the abscissas.
The storage of the information in the form of longitudinal proton magnetization is of course subject to spin-lattice relaxation T
1
(
1
H). In macromolecules such as proteins and nucleic acids, this typically limits the useful duration of the diffusion interval &Dgr;. In samples with masses on the order of 50 kDa, one has typically T
1
(
1
H)=30 ms so that the diffusion interval must be limited to about &Dgr;=30 ms (if &Dgr;=T
1
(
1
H), the loss in signal intensity is exp{&Dgr;/T
1
(
1
H)}=e
−1
=0.37). This limitation means that very small translational diffusion constants D are difficult to measure. In practice, conventional stimulated echo (STE) methods (6) involving proton magnetization using a 600 MHz spectrometer equipped with standard triple-axes gradients, have proven to be difficult if D≦10
−10
m
2
s
−1
. For instance, the diffusion coefficient of an aqueous solution of the protein Ubiquitin (D=2.4 10
−10
m
2
s
−1
at 30° C. for a mass of M=8 kDa) can be readily determined by the previously described method. The conventional stimulated echo method STE (6) has also been used for supra-molecular assemblies of high molecular weight (7), where it is possible to measure the diffusion coefficient of a highly mobile polyhistidine tag that has been attached to the protein and that has relatively narrow lines and slow proton spin-lattice relaxation. However, the construction of such fusion proteins is time-consuming. It can be shown that conventional STE methods are inadequate to determine the diffusion coefficient of an assembly of protein OmpA with detergent (D=10
−10
m
2
s
−1
for a mass of M=50 kDa) in the absence of a polyhistidine tag.
In view of these deficiencies in prior art, it is the object of the invention to present a pulsed-field gradient NMR method that allows the determination of translational diffusion coefficients or flow rates of supra-molecular assemblies or molecules with short T1(H) values, in particular of supra-molecular assemblies or molecules with M≧50 kDa.
SUMMARY OF THE INVENTION
This object is achieved, according to the invention, by a pulsed field gradient method as mentioned above, characterized in that the molecule or supra-molecular assembly contains one or several isotopes (X) of non-zero nuclear spin other than protons having longitudinal relaxation times T1(X) that are longer than the longitudinal relaxation times T1(H) of the protons, and that the information about the localization of the molecule or supra-molecular assembly during the diffusion or flow

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