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| The '''residual dipolar coupling''' between two [[Spin (physics)|spin]]s in a molecule occurs if the molecules in solution exhibit a partial alignment leading to an incomplete averaging of spatially anisotropic [[dipolar coupling]]s. | | The author's name is Andera and she believes it sounds quite great. Distributing manufacturing is how he makes a living. As a woman what she truly likes is fashion and she's been doing it for fairly a while. Alaska is where he's always been living.<br><br>Here is my web page: best psychic ([http://myoceancounty.net/groups/apply-these-guidelines-when-gardening-and-grow/ simply click the next web page]) |
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| Partial molecular alignment leads to an incomplete averaging of anisotropic magnetic interactions such as the magnetic dipole-dipole interaction (also called dipolar coupling), the [[chemical shift]] anisotropy, or the electric [[quadrupole]] interaction. The resulting so-called ''residual'' anisotropic magnetic interactions are becoming increasingly important in biomolecular [[NMR spectroscopy]].<ref>{{cite doi|10.1002/cmr.1012}}</ref>
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| [[Image:Shilirren texture.jpg|thumb|300px|Liquid crystals are commonly used to permit the observation of residual dipolar couplings in high-resolution liquid-state NMR spectra.]]
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| == History and pioneering works ==
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| NMR spectroscopy in partially oriented media was first discovered in 1963,<ref>{{cite doi|10.1103/PhysRevLett.11.462}}</ref> and in a very fundamental paper [[Alfred Saupe]] was also able to present the essential theory to describe and understand the observable phenomena only one year later.<ref>Saupe, A ''Z. Naturforsch.'' 19a, 161-171. (1964)</ref> After this initiation a flood of NMR spectra in various liquid
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| crystalline phases was reported (see ''e.g.'' <ref>{{cite doi|10.1063/1.1696638}}</ref><ref>{{cite doi|10.1021/ja00999a062}}</ref><ref>{{cite doi|10.1021/ja00988a006}}</ref><ref>{{cite doi|10.1039/qr9682200179}}</ref>).
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| A second technique for partial alignment which is not limited by a minimum anisotropy is strain-induced alignment in a gel (SAG), based on the pioneering work of Deloche and Samulski.<ref>{{cite doi|10.1021/ma50004a024}}</ref> The technique was extensively used to study the properties of polymer gels by means of high-resolution deuterium NMR,<ref>{{cite doi|10.1016/0032-3861(85)90027-8}}</ref> but only lately gel alignment was used to induce RDCs in molecules dissolved into the gel.<ref>{{cite doi|10.1023/A:1026703605147}}</ref><ref>{{cite doi|10.1021/ja002133q}}</ref> SAG allows the unrestricted scaling of alignment over a wide range and can be used for aqueous as well as organic solvents, depending on the polymer used. As a first example in organic solvents, RDC measurements in stretched polystyrene (PS) gels swollen in CDCl<sub>3</sub> were reported as a promising alignment method.<ref>{{cite doi|10.1002/anie.200352860}}</ref>
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| In 1995, James H. Prestegard and coworkers demonstrated that NMR spectra of certain proteins (in this case cyanometmyoglobin, which has a very highly anisotropic [[paramagnetic]] susceptibility), taken at very high field, may contain data that can usefully complement [[Nuclear Overhauser effect|NOE]]s in determining a tertiary fold.<ref name="Prestegard, J.H. 1995">{{cite doi|10.1073/pnas.92.20.9279}}</ref>
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| In 1996 and 1997, Adriaan Bax and coworkers measured RDCs in a [[diamagnetic]] protein ([[ubiquitin]]). The results were in good agreement with the crystal structures.<ref>{{cite doi|10.1021/ja960510m}}</ref><ref>{{cite doi|10.1006/jmre.1996.1088}}</ref>
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| ==Physics of RDC==
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| [[Image:SSNMR dip coupl vect2.png|thumb|The dipolar coupling between two nuclei depends on the distance between them, and the angle of bond relative to the external magnetic field|200px|right|The dipolar coupling between two nuclei depends on the distance between them, and the angle of bond relative to the external magnetic field]]
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| The secular dipolar coupling [[Hamiltonian (quantum mechanics)|Hamiltonian]] of two [[Spin (physics)|spins]], <math>I</math> and <math>S,</math> is given by:
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| :<math>H_\mathrm{D}={\frac{\hbar\gamma_I\gamma_S}{4\pi^2 r^3_{IS}}}[1-3 \cos^2\theta](3I_zS_z-\vec{I}\cdot \vec{S})</math>
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| where
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| *<math>\hbar</math> is the reduced [[Planck constant]].
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| *<math>\gamma_I</math> and <math>\gamma_S</math> are the [[gyromagnetic ratio]]s of spin <math>I</math> and spin <math>S</math> respectively.
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| *<math>r_{IS}</math> is the inter-spin distance.
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| *''<math>\theta</math>'' is the angle between the inter-spin vector and the external [[magnetic field]].
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| *<math>\vec{I}</math> and <math>\vec{S}</math> are vectors of [[Spin (physics)#Spin_operator|spin operators]].
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| The above equation can be rewritten in the following form:
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| :<math>H_\mathrm{D}=D_{IS}(\theta)[2I_zS_z-(I_xS_x+I_yS_y)]\!</math>
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| where
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| :<math>D_{IS}(\theta)=\frac{\hbar\gamma_I\gamma_S}{4\pi^2 r^3_{IS}}[1-3 \cos^2\theta].\!</math>
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| In isotropic solution molecular tumbling reduces the average value of <math>D_{IS}</math> to zero.
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| We thus observe no dipolar coupling. If the solution is not isotropic then the average
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| value of <math>D_{IS}</math> may be different from zero, and one may observe ''residual''
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| couplings.
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| Note that this residual dipolar coupling can be positive or negative, depending on the range of angles that are sampled.<ref>{{cite doi|10.1016/0079-6565(94)80012-X}}</ref>
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| In addition to static distance and angular information, RDCs may contain information about a molecule's internal motion. To each atom in a molecule one can associate a motion tensor '''B''', that may be computed from RDCs according to the following relation:<ref>{{cite doi|10.1021/ja0261123}}</ref>
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| :<math>D_{IS}=-\frac{\mu_0\gamma_I\gamma_S h}{(2\pi r_{IS})^3} BA\!</math>
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| where A is the molecular alignment [[tensor]].
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| The rows of B contain the motion tensors for each atom. The motion tensors also have five [[Degrees of freedom (physics and chemistry)|degrees of freedom]]. From each motion tensor, 5 parameters of interest can be computed. The variables S<sub>i</sub><sup>2</sup>, η<sub>i</sub>, α<sub>i</sub>, β<sub>i</sub> and γ<sub>i</sub> are used to denote these 5 parameters for atom i. S<sub>i</sub><sup>2</sup> is the magnitude of atom i’s motion; η<sub>i</sub> is a measure of the anisotropy of atom i’s motion; α<sub>i</sub> and β<sub>i</sub> are related to the polar coordinates of the bond vector expressed in the initial arbitrary reference frame (i.e., the PDB frame). If the motion of the atom is anisotropic (i.e., η<sub>i</sub> = 0), the final parameter, γ<sub>i</sub> measures the principal orientation of the motion.
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| Note that the RDC-derived motion parameters are local measurements.
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| ==Measurement of RDC==
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| [[Image:800px-RDc-effects-HSQC-vertical.png|thumb|200px|right|Panel C depicts the effect of N-H residual dipolar coupling on undecoupled HSQC spectrum. A: no splitting, B: J-splitting, C: JD-splitting]]
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| Any RDC measurement in solution consists of two steps, aligning the molecules and NMR studies:
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| ===Methods for aligning molecules===
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| For [[diamagnetic]] molecules at moderate field strengths, molecules have little preference in orientation, the tumbling samples a nearly isotropic distribution, and average [[dipolar coupling]]s goes to zero. Actually, most molecules have preferred orientations in the presence of a magnetic field, because most have anisotropic [[magnetic susceptibility]] [[tensor]]s, Χ.<ref name="Prestegard, J.H. 1995"/>
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| The method is most suitable for systems with large values for magnetic susceptibility tensor. This includes: Protein-nucleic acid complex, [[nucleic acids]], proteins with large number of [[aromatic]] residues, [[porphyrin]] containing proteins and metal binding proteins (metal may be replaced by [[lanthanide]]s).
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| For a fully oriented molecule, the dipolar coupling for an <sup>1</sup>H-<sup>15</sup>N [[amide|amide group]] would be over 20 [[Hertz|kHz]], and a pair of protons separated by 5 Å would have up to ~1 kHz coupling. However the degree of alignment achieved by applying magnetic field is so low that the largest <sup>1</sup>H-<sup>15</sup>N or <sup>1</sup>H-<sup>13</sup>C dipolar couplings are <5 Hz.<ref name="M.R. Hansen 1998">{{cite doi|10.1038/4176}}</ref> Therefore many different alignment media have been designed:
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| *Lipid bicelles (with large magnetic susceptibility): measured RDCs were of the order of hundreds of Hz.<ref>{{cite doi|10.1021/ja00106a078}}</ref>
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| *[[Liquid crystal]]line bicelles: measured RDCs were between -40 and +20 Hz.<ref>{{cite doi|10.1126/science.278.5340.1111}}</ref>
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| *filamentous Pf1 bacteriophage (large anisotropic magnetic susceptibility): <sup>1</sup>H-<sup>1</sup>H through space dipolar coupling were measured.<ref name="M.R. Hansen 1998"/>
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| *DNA nanotubes (compatible with detergents used to solubilize membrane proteins)<ref>{{cite doi|10.1073/pnas.0700930104}}</ref>
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| ===NMR experiments===
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| There are numerous methods that have been designed to accurately measure coupling constant between nuclei.<ref>{{cite doi|10.1017/S0033583500003656}}</ref> They have been classified into two groups: ''frequency based methods'' where separation of peaks centers (splitting) is measured in a frequency domain, and ''intensity based methods'' where the coupling is extracted from the resonance intensity instead of splitting. The two methods complement each other as each of them is subject to a different kind of systematic errors. Here are the prototypical examples of NMR experiments belonging to each of the two groups:
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| * ''Intensity methods'': quantitative J-modulation experiment and phase modulated methods
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| * ''frequency resolved methods'': SCE-[[HSQC]], [[E. COSY]] and spin state selective experiments
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| ==RDC and structural biology ==
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| RDC measurement provides information on the global [[Protein structure|folding]] of the protein or protein complex. As opposed to traditional NOE based [[Protein nuclear magnetic resonance spectroscopy|NMR structure determinations]], RDCs provide long distance structural information. It also provides information about the dynamics in molecules on time scales slower than nanoseconds.
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| ===RDC and studies of biomolecular structure ===
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| [[Image:RDC and protein structure.png|thumb|300px|The blue arrows represent the orientation of the N - H bond of selected peptide bonds. By determining the orientation of a sufficient number of bonds relative to the external magnetic field, the structure of the protein can be determined. From PDB 1KBH.]]
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| Most NMR studies of protein structure are based on analysis of the [[Nuclear Overhauser effect]], NOE, between different protons in the protein. Because the NOE depends on the inverted sixth power of the distance between the nuclei, r<sup>−6</sup>, NOEs can be converted into distance restraints that can be used in [[molecular dynamics]]-type structure calculations. RDCs provide orientational restraints rather than distance restraints, and has several advantages over NOEs:
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| *RDCs give information about the angle relative to the external magnetic field, which means that it can give information about the relative orientation of parts of the molecule that are far apart in the structure.
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| *In large molecules (>25kDa) it is often difficult to record NOEs due to [[spin diffusion]]. This is not a problem with RDCs.
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| *Analysis of a high number of NOEs can be very time consuming.
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| Provided that a very complete set of RDCs is available, it has been demonstrated for several model systems that molecular structures can be calculated exclusively based on these anisotropic interactions, without recourse to NOE restraints. However, in practice, this is not achievable and RDC is used mainly to refine a structure determined by NOE data and J-couplings. One problem with using dipolar couplings in structure determination is that a dipolar coupling does not uniquely describe an internuclear vector orientation. Moreover if a very small set of dipolar couplings are available, the refinement may lead to a structure worse than the original one. For a protein with N aminoacids, 2N RDC constraint for backbone is the minimum needed for an accurate refinement.<ref name="Alexander Grishaev 2005">{{cite doi|10.1016/j.sbi.2005.08.006}}</ref>
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| [[Image:RDC curves on NMRmodels 1d3z D58NH.jpg|thumb|right|300px| RDC target curves for the N-H vector of Asp58 in a tight 10-model ensemble for ubiquitin (PDB:1D3Z)]]
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| The information content of an individual RDC measurement for a specific bond vector (such as a specific backbone NH bond in a protein molecule) can be understood by showing the target curve that traces out directions of perfect agreement between the observed RDC value and the value calculated from the model. Such a curve (see figure) has two symmetrical branches that lie on a sphere with its polar axis along the magnetic field direction. Their height from the sphere's equator depends on the magnitude of the RDC value and their shape depends on the "rhombicity" (asymmetry) of the molecular alignment tensor. If the molecular alignment were completely symmetrical around the magnetic field direction, the target curve would just consist of two circles at the same angle from the poles as the angle <math>\theta</math> that the specific bond vector makes to the applied magnetic field.<ref name="Alexander Grishaev 2005"/>
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| In the case of elongated molecules such as [[RNA]], where local torsional information and short distances are not enough to constrain the structures, RDC measurements can provide information about the orientations of specific [[chemical bond]]s throughout a nucleic acid with respect to a single coordinate frame. Particularly, RNA molecules are [[proton]]-poor and overlap of [[ribose]] resonances make it very difficult to use [[J-coupling]] and [[Nuclear Overhauser effect|NOE]] data to determine the structure. Moreover, RDCs between nuclei with a distance larger than 5-6 Å can be detected. This distance is too much for generation of NOE signal. This is because RDC is proportional to r<sup>−3</sup> whereas NOE is proportional to r<sup>−6</sup>.
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| RDC measurements have recently been proved useful for a rapid determination of the relative orientations of units of known structures in proteins.<ref>{{cite doi|10.1074/jbc.M414300200}}</ref> In principle, the orientation of a structural subunit, which may be as small as a turn of a helix or as large as an entire domain, can be established from as few as five RDCs per subunit.<ref name="Alexander Grishaev 2005"/>
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| ===RDC and protein dynamics ===
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| Although [[crystallography|crystallographic]] B-factors and [[Relaxation (NMR)|NMR spin relaxation]] analysis can be used to measure motional parameters, they suffer from several drawbacks. For example they assume dynamic independence of different regions of the molecule under investigation.{{citation needed|date=November 2011}} Techniques like [[quasielastic scattering|quasielastic]] and [[inelastic scattering|inelastic]] [[neutron scattering]], diffuse [[X-ray scattering]], inelastic [[Rudolf Mößbauer|Mössbauer]] scattering and [[dielectric spectroscopy]]<ref>{{cite doi|10.1021/ma070792i}}</ref> can in principle provide information about correlated motions. However interpretation of data on molecular level is often difficult. While [[molecular dynamics|molecular dynamic simulation]] are very successful in predicting pico to nano second motions, they are often limited in their abilities in investigating "long"-time scale motions{{citation needed|date=November 2011}}. In the recent years success has been reported by several investigators in predicting slow conformational changes in proteins at the microsecond-millisecond time-scales (or the long time-scale motions) that are related to catalysis in enzymes such as [[dihydrofolate reductase]] and [[cyclophilin]] A using theoretical techniques.{{citation needed|date=November 2011}} These slow conformational changes have been verified by NMR techniques.{{citation needed|date=November 2011}}
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| For the first time in 1997, Prestegard ''et al.'' investigated slow dynamics (>10<sup>-9</sup> s) in [[myoglobin]] by RDC measurement.<ref>{{cite doi|10.1038/nsb0497-292}}</ref> In general, internal motion of a bond vector relative to the molecular alignment frame scales the size of the RDC relative to a static average orientation. This scaling factor is dependent on both the amplitude and the direction of such motion relative to the alignment tensor; scaling factors therefore will differ with the alignment medium used. RDC approach to studying dynamics is most robust for large-amplitude processes (> 20°).<ref>{{cite doi|10.1016/j.jmr.2005.01.001}}</ref>
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| == Further reading ==
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| '''Books''':
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| *Emsley, J. W.; Lindon, J. C. NMR Spectroscopy using liquid crystal solvents; Pergamon Press: Oxford, U.K., 1975.
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| '''Review papers''':
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| *Ad Bax and Alexander Grishaev, ''Current Opinion in Structural Biology'', 15:563–570 (2005)
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| *Rebecca S. Lipsitz and Nico Tjandra, ''Annu. Rev. Biophys. Biomol. Struct''. 33:387–413 (2004)
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| '''Classic papers''':
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| *Saupe, A.; Englert, G. ''Phys. ReV. Lett.'' 11, 462-464 (1963).
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| *Saupe, A. ''Z. Naturforsch.'' 19a, 161-171 (1964).
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| *Deloche, B.; Samulski, E. T. ''Macromolecules'' 14, 575-581 (1981).
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| *Nico Tjandra and Ad Bax. ''Science'' Vol. 278. no. 5340, pp. 1111 – 1114 (1997)
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| *Ad Bax ''et al.'' ''Nature Structural Biology'' 4, 732 - 738 (1997)
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| *J. R. Tolman ''et al.'' ''Nature Structural Biology'' 4, 292 - 297 (1997)
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| *Tjandra, N. & Bax, A., ''J. Magn. Reson.'' 124, 512−515 (1997).
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| *Tjandra, N., Grzesiek, S. & Bax, A., ''J. Am. Chem. Soc.'' 118, 6264−6272 (1996).
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| *Tolman, J.R. & Prestegard, J.H., ''J. Magn. Reson.'' B 112, 245−252 (1996).
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| *Tolman, J.R., Flanagan, J.M., Kennedy, M.A. & Prestegard, J.H., ''Proc. Natl. Acad. Sci. U.S.A.'' 92, 9279−9283 (1995).
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| *Sanders, C.R., Hare, B.J., Howard, K.P. & Prestegard, J.H., ''Prog. Nucl. Magn. Reson. Spectrosc.'' 26, 421−444 (1994).
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| *Bastiaan, E. W., Maclean, C., Van Zijl, P. C. M. & Bothner-By, A. A. ''Annu. Rep. NMR Spectrosc.'' 19, 35-77.(1987)
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| == References==
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| {{reflist}}
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| == See also ==
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| *[[Magnetic dipole–dipole interaction]]
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| *[[Residual chemical shift anisotropy]] (rCSA)
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| *[[Solid-state nuclear magnetic resonance]] (ssNMR)
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| [[Category:Nuclear magnetic resonance]]
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| [[Category:Protein structure]]
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