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{{NMR-experiment}}
NMR spectroscopy allows measurement of the coefficient of self-diffusion ('''D<sub>s</sub>''') which is defined<cite>iupac</cite> as the translational diffusion coefficient at zero gradient of the chemical potential. Most frequently that condition simply implies zero concentration gradient.

D<sub>s</sub> is related to the hydrodynamic properties and size of the molecule indicative of its aggregation state. Unlike ultracentrifugation or dynamic light scattering, both also measuring D<sub>s</sub>, NMR methods work at mM concentration, i.e. in the conditions used for structural work by NMR.

==LED==
LED stands for '''longitudinal encode-decode''' experiment. The LED experiment is an evolutionary improvement of the PFGSTE (stimulated echo: {{90}}-&tau;<sub>PFG</sub>-{{90}}-T-{{90}}-&tau;<sub>PFG</sub>-acquire) experiment proposed by Tanner in 1970<cite>tanner70ste</cite>.
In LED experiments<cite>led91</cite> magnetization is stored along the z-axis during most of the pulse sequence, so [[T1 relaxation]] is predominant. Since in macromolecules the T1 relaxation is slower than the [[T2 relaxation]], the LED experiment is better suited to the measurement of D<sub>s</sub> of slower diffusing molecules where longer "diffusion delay" is required to detect attenuation of the signal.

The water-sLED experiment<cite>sled95</cite> is a modification of the LED experiment<cite>led91</cite> with added water suppression ([[Water flip-back]] and [[RAW]]). water-sLED allows determination of D<sub>s</sub> for molecules with molecular weights of up to ~40 kDa.

The amplitude of the echo in these experiments follows the equation below:

<math>A(2\tau) = A(0) e^{-(\gamma \delta G)^2(\Delta-\frac{\delta}{3})D_s}</math>

Where:
*&gamma; - [[gyromagnetic ratio]] of the nucleus
*&delta; - duration of the [[PFG]]
*G - gradient strength
*D<sub>s</sub> - constant of self-diffusion
*&Delta; time between beginnings of the two gradient pulses

==BPP-SED==
The BPP-SED experiment <cite>bppsed99</cite> combines the BPP-LED and SED (selective echo dephasing) water suppression schemes; it is designed to measure self-diffusion constants of biomolecules in up to 95% {{H2O}}. This experiment requires a tri-axial PFG probe as gradients along the x,y,z axes are used.

==References==
<biblio>
#bppsed99 bibtex=@article{krishnan1999ies,
  title={{An improved experimental scheme to measure self-diffusion coefficients of biomolecules with an advantageous use of radiation damping}},
  author={Krishnan, VV and Thornton, K.H. and Cosman, M.},
  journal={Chemical Physics Letters},
  volume={302},
  number={3-4},
  pages={317--323},
  year={1999},
  publisher={Elsevier},
  url={http://dx.doi.org/10.1016/S0009-2614(99)00143-8}
}
#hahn50echo bibtex=@article{hahn1950se,
  title={{Spin Echoes}},
  author={Hahn, E.L.},
  journal={Physical Review},
  volume={80},
  number={4},
  pages={580--594},
  year={1950},
  publisher={APS},
  url={http://dx.doi.org/10.1103/PhysRev.80.580}
}
#tanner70ste bibtex=@article{tanner1970use,
  title={{Use of the Stimulated Echo in NMR Diffusion Studies}},
  author={Tanner, JE},
  journal={Journal of Chemical Physics},
  volume={52},
  pages={2523--2526},
  year={1970},
  url={http://dx.doi.org/10.1063/1.1673336}
}
#iupac [http://goldbook.iupac.org/S05582.html IUPAC definition] of self-diffusion coefficient
#viel_dosy [[media:stephane_viel_dosy.ppt|Lecture on DOSY]] by [[User:Stéphane Viel|Prof. Stéphane Viel]]
#sled95 bibtex=@article{altieri1995abs,
  title={{Association of Biomolecular Systems via Pulsed Field Gradient NMR Self-Diffusion Measurements}},
  author={Altieri, A.S. and Hinton, D.P. and Byrd, R.A.},
  journal={Journal of the American Chemical Society},
  volume={117},
  number={28},
  pages={7566--7567},
  year={1995},
  publisher={American Chemical Society},
  url={http://dx.doi.org/10.1021%2Fja00133a039}
}
#led91 bibtex=@article{gibbs1991pne,
  title={{A PFG NMR experiment for accurate diffusion and flow studies in the presence of Eddy currents}},
  author={GIBBS, SJ and JOHNSON, CS},
  journal={Journal of magnetic resonance},
  volume={93},
  number={2},
  pages={395--402},
  year={1991},
  publisher={Academic Press}
}
#stilbs87 bibtex=@article{stilbs1987ftp,
  title={Fourier transform pulsed-gradient spin-echo studies of molecular diffusion},
  author={STILBS, P.},
  journal={Progress in nuclear magnetic resonance spectroscopy},
  volume={19},
  number={1},
  pages={1-45},
  year={1987},
  publisher={Elsevier Science},
  url={http://dx.doi.org/10.1016/0079-6565(87)80007-9}
}
#price97 bibtex=@article{Price:1997cmr,
	Abstract = {Translational diffusion is the most fundamental form of transport in chemical and biochemical systems. Pulsed-field gradient nuclear magnetic resonance provides a convenient and noninvasive means for measuring translational motion. In this method the attenuation of the echo signal from a Hahn spin-echo pulse sequence containing a magnetic field gradient pulse in each ? period is used to measure the displacement of the observed spins. In the present article, the physical basis of this method is considered in detail. Starting from the Bloch equations containing diffusion terms, the (analytical) equation linking the echo attenuation to the diffusion of the spin for the case of unrestricted isotropic diffusion is derived. When the motion of the spin occurs within a confined geometry or is anisotropic, such as in in vivo systems, the echo attenuation also yields information on the surrounding structure, but as the analytical approach becomes mathematically intractable, approximate or numerical means must be used to extract the motional information. In this work, two common approximations are considered and their limitations are examined. Measurements in anisotropic systems are also considered in some detail},
	Author = {Price, William S.},
	Journal = {Concepts in Magnetic Resonance},
	Keywords = {Pulsed field-gradient NMR;self-diffusion},
	Number = {5},
	Pages = {299-336},
	Title = {Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part 1. Basic theory},
	Url = {http://dx.doi.org/10.1002/(SICI)1099-0534(1997)9:5<299::AID-CMR2>3.0.CO;2-U},
	Volume = {9},
	Year = {1997}}
#price98 bibtex=@article{Price:1998cmr,
	Author = {Price, William S.},
	Journal = {Concepts in Magnetic Resonance},
	Keywords = {Pulsed field-gradient NMR;self-diffusion},
	Number = {4},
	Pages = {197-237},
	Title = {Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part II. Experimental aspects},
	Url = {http://dx.doi.org/10.1002/(SICI)1099-0534(1998)10:4<197::AID-CMR1>3.0.CO;2-S},
	Volume = {10},
	Year = {1998}}
#johhnson99 bibtex=@article{JohnsonJr.:1999ne,
	Author = {Johnson, Jr. , Charles S.},
	Journal = {Progress in Nuclear Magnetic Resonance Spectroscopy},
	Pages = {203-256},
	Title = {Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications},
	Volume = {34},
	Year = {1999}
        url={http://dx.doi.org/10.1016/S0079-6565(99)00003-5}}
#antalek02 bibtex=@article{Antalek:2002os,
	Abstract = {Pulsed gradient spin echo NMR is a powerful technique for measuring diffusion coefficients. When coupled with appropriate data processing schemes, the technique becomes an exceptionally valuable tool for mixture analysis, the separation of which is based on the molecular size. Extremely fine differentiation may be possible in the diffusion dimension but only with high-quality data. For fully resolved resonances, components with diffusion coefficients that differ by less than 2% may be distinguished in mixtures. For highly overlapped resonances, the resolved spectra of pure components with diffusion coefficients that differ by less than 30% may be obtained. In order to achieve the best possible data quality one must be aware of the primary sources of artifacts and incorporate the necessary means to alleviate them. The origin of these artifacts are described, along with the methods necessary to observe them. Practical solutions are presented. Examples are shown that demonstrate the effects of the artifacts on the acquired data set. Many mixture analysis problems may be addressed with conventional high resolution pulsed field gradient probe technology delivering less than 0.5 T m-1 (50 G cm-1)},
      Title = {Using pulsed gradient spin echo NMR for chemical mixture analysis: How to obtain optimum results},	
       Author = {Antalek, Brian},
	Journal = {Concepts in Magnetic Resonance},
	Keywords = {Pulsed field-gradient NMR;signal processing},
	Number = {4},
	Pages = {225-258},
	Url = {http://dx.doi.org/10.1002/cmr.10026},
	Volume = {14},
	Year = {2002}}
#morris02 bibtex=@incollection{Morris:2002enc,
	Address = {Chichester},
	Author = {Morris, Gareth A.},
	Booktitle = {Encyclopedia of Nuclear Magnetic Resonance},
	Date-Added = {2006-04-01 20:45:55 +0200},
	Date-Modified = {2006-06-01 14:39:56 +0200},
	Editor = {Grant, D. M. and Harris, K. R.},
	Keywords = {DOSY},
	Local-Url = {file://localhost/Users/dolcegabanna/Documents/Universite%CC%81/biblio/MorrisGA.DOSY.Encyc.pdf},
	Pages = {35-44},
	url={http://dx.doi.org/10.1002/9780470034590.emrstm0119}
        Publisher = {John Wiley \& Sons, Ltd},
	Title = {Diffusion-Ordered NMR Spectroscopy},
	Volume = {9},
	Year = {2002}}
#armst03 bibtex=@article{Armstrong:2003dosy,
	Author = {Armstrong, Geoffrey S. and Loening, Nikolaus M. and Curtis, Joseph E. and Shaka, A. J. and Mandelshtam, Vladimir A.},
	Journal = {Journal of Magnetic Resonance},
        Number = {1},
	Pages = {139-148},
	Title = {Processing DOSY spectra using the regularized resolvent transform},
	Url = {http://dx.doi.org/doi:10.1016/S1090-7807(03)00126-5 },
	Volume = {163},
	Year = {2003}}
#viel03 bibtex=@article{SVielPNAS2003,
	Abstract = {We introduce an analytical method that combines in one pot the advantages of column chromatography separation and NMR structural analysis. The separation of the NMR spectra of the components of a mixture can be achieved according to their apparent diffusion rates [James, T. L. and McDonald, G. G. (1973) J. Magn. Reson. 58, 58-61]. We show that the separation of the spectral components, corresponding to single molecular species, can be  enhanced by order of magnitudes upon addition of a typical stationary phase used in HPLC. The solid phase imbibed by the mixture for analysis is an heterogeneous ensemble, so that solid-state NMR methods (high-resolution magic angle spinning) are necessary to recover high-resolution spectra. We demonstrate applications of this combination of high-resolution magic angle spinning and NMR diffusometry on test mixtures for direct (silica gel) and inverse (C18) columns. However, many common chromatographic supports available for HPLC should be readily adaptable for use with this technique.
},
	Author = {Viel, Stephane and Ziarelli, Fabio and Caldarelli, Stefano},
	Date-Modified = {1970-01-01 01:31:46 +0100},
	Eprint = {http://www.pnas.org/cgi/reprint/100/17/9696.pdf},
	Journal = {PNAS},
	Local-Url = {file://localhost/Users/dolcegabanna/Documents/Universite%CC%81/biblio/Viel.PNAS.100.9696.pdf},
	Number = {17},
	Pages = {9696-9698},
	Title = {Enhanced diffusion-edited NMR spectroscopy of mixtures using chromatographic stationary phases},
	Url = {http://www.pnas.org/cgi/content/abstract/100/17/9696},
	Volume = {100},
	Year = {2003}}
#cohen05 bibtex=@article{Cohen:2005tg,
	Abstract = {Intermolecular interactions in solution play an important role in molecular recognition, which lies at the heart of supramolecular and combinatorial chemistry. Diffusion NMR spectroscopy gives information over such interactions and has become the method of choice for simultaneously measuring diffusion coefficients of multicomponent systems. The diffusion coefficient reflects the effective size and shape of a molecular species. Applications of this technique include the estimation of association constants and mapping the intermolecular interactions in multicomponent systems as well as investigating aggregation, ion pairing, encapsulation, and the size and structure of labile systems. Diffusion NMR spectroscopy can also be used to virtually separate mixtures and screen for specific ligands of different receptors, and may assist in finding lead compounds.},
	Author = {Cohen, Yoram and Avram, Liat and Frish, Limor},
	Journal = {Angewandte Chemie International Edition},
	Number = {4},
	Pages = {520-540},
	Title = {Diffusion NMR Spectroscopy in Supramolecular and Combinatorial Chemistry: An Old Parameter-New Insights},
	Url = {http://dx.doi.org/10.1002/anie.200300637},
	Volume = {44},
	Year = {2005}}
#brand05 bibtex=@article{Brand:2005eu,
	Author = {Brand, Torsten  and Cabrita, Eurico J. and Berger, Stefan},
	Journal = {Progress in Nuclear Magnetic Resonance Spectroscopy},
	Pages = {159-196},
	Title = {Intermolecular interaction as investigated by NOE and diffusion studies},
	Volume = {46},
	Year = {2005}}
#thureau bibtex=@article{ThureauP.-b513580j,
	Abstract ={The exchange rates of the amido-protons of uracil with water were determined by NMR diffusion experiments and the results showed a factor 2 difference in lability between them, which was confirmed by more classical 2D-NMR exchange experiments.}
        Author = {Thureau, P. and Ancian, B. and Viel, S. and Thevand, A.},
	Journal = {Chemical Communications},
	Keywords = {chemical exchanges;Pulsed field-gradient NMR;nucleic acid bases},
	Title = {Determining chemical exchange rates of the uracil labile protons by NMR diffusion experiments},
	Url = {http://dx.doi.org/10.1039/b513580j}
        Year = {2006}}
#viel08 bibtex=@article{Viel:2008nx,
	Author = {Viel, Stephane and Ziarelli, Fabio and Pages, Guilhem and Carrara, Caroline and Caldarelli, Stefano},
	Abstract ={Several investigations have recently reported the combined use of pulsed field gradient (PFG) with magic angle spinning (MAS) for the analysis of molecular mobility in heterogeneous materials. In contrast, little attention has been devoted so far to delimiting the role of the extra force field induced by sample rotation on the significance and reliability of self-diffusivity measurements. The main purpose of this work is to examine this phenomenon by focusing on pure liquids for which its impact is expected to be largest. Specifically, we show that self-diffusion coefficients can be accurately determined by PFG MAS NMR diffusion measurements in liquids, provided that specific experimental conditions are met. First, the methodology to estimate the gradient uniformity and to properly calibrate its absolute strength is briefly reviewed and applied on a MAS probe equipped with a gradient coil aligned along the rotor spinning axis, the so-called ‘magic angle gradient’ coil. Second, the influence of MAS on the outcome of PFG MAS diffusion measurements in liquids is investigated for two distinct typical rotors of different active volumes, 12 and 50 μL. While the latter rotor led to totally unreliable results, especially for low viscosity compounds, the former allowed for the determination of accurate self-diffusion coefficients both for fast and slowly diffusing species. Potential implications of this work are the possibility to measure accurate self-diffusion coefficients of sample-limited mixtures or to avoid radiation damping interferences in NMR diffusion measurements. Overall, the outlined methodology should be of interest to anyone who strives to improve the reliability of MAS diffusion studies, both in homogeneous and heterogeneous media.}
        Journal = {Journal of Magnetic Resonance},
	Keywords = {HR MAS; Self-diffusion coefficients; Liquids; Gradient uniformity; Magic angle gradient},
	Number = {1},
	Pages = {113-123},
	Title = {Pulsed field gradient magic angle spinning NMR self-diffusion measurements in liquids},
	Ty = {JOUR},
	Url = {http://dx.doi.org/doi:10.1016/j.jmr.2007.10.010},
	Volume = {190},
	Year = {2008},
</biblio>
[[Category:NMR application]]
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