Residual dipolar coupling
Encyclopedia
The residual dipolar coupling between two spin
s in a molecule occurs if the molecules in solution exhibit a partial alignment leading to an incomplete averaging of spatially anisotropic dipolar couplings.
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
.
was also able to present the essential theory to describe and understand the observable phenomena only one year later. After this initiation a flood of NMR spectra in various liquid
crystalline phases was reported (see e.g. ).
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. The technique was extensively used to study the properties of polymer gels by means of high-resolution deuterium NMR, but only lately gel alignment was used to induce RDCs in molecules dissolved into the gel. 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 CDCl3 were reported as a promising alignment method.
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 NOE
s in determining a tertiary fold.
In 1996 and 1997, Tjandra et al. measured RDCs in a diamagnetic protein (ubiquitin
). The results were in good agreement with crystal structure.
of two spin
s, I and S is as follows:
where:
The above equation can be rewritten in the following form:
The first term on the left is similar to the hamiltonian for J-coupling
, which is responsible for splitting of lines in NMR spectrum. In other words coupling constant will differ when the molecules in the sample are aligned (J + 2D) or not (J). The difference is what is named as residual dipolar coupling:
Note that residual dipolar coupling can be positive or negative, depending on the range of angles that are sampled.
In addition to static distance and angular information, RDC may contain information about internal motions in molecules. To each atom in a molecule one can associate a motion tensor B, that may be computed from RDCs according to the following relation:
where A is the molecular alignment tensor
.
The rows of B contain the motion tensors for each atom. The motion tensors also have five degrees of freedom
. From each motion tensor, 5 parameters of interest can be computed. The variables Si2, ηi, αi, βi and γi are used to denote these 5 parameters for atom i. Si2 is the magnitude of atom i’s motion; ηi is a measure of the anisotropy of atom i’s motion; αi and βi 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., ηi = 0), the final parameter, γi measures the principal orientation of the motion.
Note that the RDC-derived motion parameters are local measurements.
tensor
s, Χ.
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).
For a fully oriented molecule, the dipolar coupling for an 1H-15N amide group would be over 20 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 1H-15N or 1H-13C dipolar couplings are <5 Hz. Therefore many different alignment media have been designed:
of the protein or protein complex. As opposed to traditional NOE based NMR structure determinations
, RDCs provide long distance structural information. It also provides information about the dynamics in molecules on time scales slower than nanoseconds.
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−6, 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:
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.
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 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−3 whereas NOE is proportional to r−6.
RDC measurements have recently been proved useful for a rapid determination of the relative orientations of units of known structures in proteins. 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.
B-factors and 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. Techniques like quasielastic
and inelastic
neutron scattering
, diffuse X-ray scattering, inelastic Mossbauer
scattering and dielectric spectroscopy
can in principle provide information about correlated motions. However interpretation of data on molecular level is often difficult. While 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. 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. These slow conformational changes have been verified by NMR techniques.
For the first time in 1997, Prestegard et al. investigated slow dynamics (>10−9 s) in myoglobin
by RDC measurement. 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°).
Review papers:
Classic papers:
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
s in a molecule occurs if the molecules in solution exhibit a partial alignment leading to an incomplete averaging of spatially anisotropic dipolar couplings.
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
Chemical shift
In nuclear magnetic resonance spectroscopy, the chemical shift is the resonant frequency of a nucleus relative to a standard. Often the position and number of chemical shifts are diagnostic of the structure of a molecule...
anisotropy, or the electric quadrupole
Quadrupole
A quadrupole or quadrapole is one of a sequence of configurations of—for example—electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure reflecting various orders of complexity.-Mathematical...
interaction. The resulting so-called residual anisotropic magnetic interactions are becoming increasingly important in biomolecular NMR spectroscopy
NMR spectroscopy
Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy, is a research technique that exploits the magnetic properties of certain atomic nuclei to determine physical and chemical properties of atoms or the molecules in which they are contained...
.
History and pioneering works
NMR spectroscopy in partially oriented media was first discovered in 1963, and in a very fundamental paper Alfred SaupeAlfred Saupe
-Biography:Alfred Saupe was a German Physicist born in Badenweiler, who laid groundbreaking work in the area of liquid crystal studies....
was also able to present the essential theory to describe and understand the observable phenomena only one year later. After this initiation a flood of NMR spectra in various liquid
crystalline phases was reported (see e.g. ).
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. The technique was extensively used to study the properties of polymer gels by means of high-resolution deuterium NMR, but only lately gel alignment was used to induce RDCs in molecules dissolved into the gel. 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 CDCl3 were reported as a promising alignment method.
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 NOE
Nuclear Overhauser effect
The Nuclear Overhauser Effect is the transfer of nuclear spin polarization from one nuclear spin population to another via cross-relaxation. It is a common phenomenon observed by nuclear magnetic resonance spectroscopy. The theoretical basis for the NOE was described and experimentally verified...
s in determining a tertiary fold.
In 1996 and 1997, Tjandra et al. measured RDCs in a diamagnetic protein (ubiquitin
Ubiquitin
Ubiquitin is a small regulatory protein that has been found in almost all tissues of eukaryotic organisms. Among other functions, it directs protein recycling.Ubiquitin can be attached to proteins and label them for destruction...
). The results were in good agreement with crystal structure.
Physics of RDC
The general form for the dipolar coupling hamiltonianHamiltonian (quantum mechanics)
In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...
of two spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
s, I and S is as follows:
where:
- h is the Planck's constant.
- γ is the gyromagnetic ratio.
- r is the inter-spin distance.
- θ is the angle between the inter-spin vector and the external magnetic fieldMagnetic fieldA magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
. - I and S are spin operators.
The above equation can be rewritten in the following form:
The first term on the left is similar to the hamiltonian for J-coupling
J-coupling
J-coupling is the coupling between two nuclear spins due to the influence of bonding electrons on the magnetic field running between the two nuclei. J-coupling contains information about dihedral angles, which can be estimated using the Karplus equation...
, which is responsible for splitting of lines in NMR spectrum. In other words coupling constant will differ when the molecules in the sample are aligned (J + 2D) or not (J). The difference is what is named as residual dipolar coupling:
Note that residual dipolar coupling can be positive or negative, depending on the range of angles that are sampled.
In addition to static distance and angular information, RDC may contain information about internal motions in molecules. To each atom in a molecule one can associate a motion tensor B, that may be computed from RDCs according to the following relation:
where A is the molecular alignment tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...
.
The rows of B contain the motion tensors for each atom. The motion tensors also have five degrees of freedom
Degrees of freedom (physics and chemistry)
A degree of freedom is an independent physical parameter, often called a dimension, in the formal description of the state of a physical system...
. From each motion tensor, 5 parameters of interest can be computed. The variables Si2, ηi, αi, βi and γi are used to denote these 5 parameters for atom i. Si2 is the magnitude of atom i’s motion; ηi is a measure of the anisotropy of atom i’s motion; αi and βi 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., ηi = 0), the final parameter, γi measures the principal orientation of the motion.
Note that the RDC-derived motion parameters are local measurements.
Measurement of RDC
Any RDC measurement in solution consists of two steps, aligning the molecules and NMR studies:Methods for aligning molecules
For diamagnetic molecules at moderate field strengths, molecules have little preference in orientation, the tumbling samples a nearly isotropic distribution, and average dipolar couplings goes to zero. Actually, most molecules have preferred orientations in the presence of a magnetic field, because most have anisotropic magnetic susceptibilityMagnetic susceptibility
In electromagnetism, the magnetic susceptibility \chi_m is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field...
tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...
s, Χ.
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
Porphyrin
Porphyrins are a group of organic compounds, many naturally occurring. One of the best-known porphyrins is heme, the pigment in red blood cells; heme is a cofactor of the protein hemoglobin. Porphyrins are heterocyclic macrocycles composed of four modified pyrrole subunits interconnected at...
containing proteins and metal binding proteins (metal may be replaced by lanthanide
Lanthanide
The lanthanide or lanthanoid series comprises the fifteen metallic chemical elements with atomic numbers 57 through 71, from lanthanum through lutetium...
s).
For a fully oriented molecule, the dipolar coupling for an 1H-15N amide group would be over 20 kHz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
, 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 1H-15N or 1H-13C dipolar couplings are <5 Hz. Therefore many different alignment media have been designed:
- Lipid bicelles (with large magnetic susceptibility): measured RDCs were of the order of hundreds of Hz.
- Liquid crystalLiquid crystalLiquid crystals are a state of matter that have properties between those of a conventional liquid and those of a solid crystal. For instance, an LC may flow like a liquid, but its molecules may be oriented in a crystal-like way. There are many different types of LC phases, which can be...
line bicelles: measured RDCs were between -40 and +20 Hz. - filamentous Pf1 bacteriophage (large anisotropic magnetic susceptibility): 1H-1H through space dipolar coupling were measured.
NMR experiments
There are numerous methods that have been designed to accurately measure coupling constant between nuclei. 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:- Intensity methods: quantitative J-modulation experiment and phase modulated methods
- frequency resolved methods: SCE-HSQC, E. COSY and spin state selective experiments
RDC and structural biology
RDC measurement provides information on the global foldingProtein structure
Proteins are an important class of biological macromolecules present in all organisms. Proteins are polymers of amino acids. Classified by their physical size, proteins are nanoparticles . Each protein polymer – also known as a polypeptide – consists of a sequence formed from 20 possible L-α-amino...
of the protein or protein complex. As opposed to traditional NOE based NMR structure determinations
Protein nuclear magnetic resonance spectroscopy
Nuclear magnetic resonance spectroscopy of proteins is a field of structural biology in which NMR spectroscopy is used to obtain information about the structure and dynamics of proteins. The field was pioneered by Richard R. Ernst and Kurt Wüthrich, among others...
, RDCs provide long distance structural information. It also provides information about the dynamics in molecules on time scales slower than nanoseconds.
RDC and studies of biomolecular structure
Nuclear Overhauser effect
The Nuclear Overhauser Effect is the transfer of nuclear spin polarization from one nuclear spin population to another via cross-relaxation. It is a common phenomenon observed by nuclear magnetic resonance spectroscopy. The theoretical basis for the NOE was described and experimentally verified...
, NOE, between different protons in the protein. Because the NOE depends on the inverted sixth power of the distance between the nuclei, r−6, NOEs can be converted into distance restraints that can be used in molecular dynamics
Molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...
-type structure calculations. RDCs provide orientational restraints rather than distance restraints, and has several advantages over NOEs:
- 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.
- In large molecules (>25kDa) it is often difficult to record NOEs due to spin diffusion. This is not a problem with RDCs.
- Analysis of a high number of NOEs can be very time consuming.
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.
In the case of elongated molecules such as RNA
RNA
Ribonucleic acid , or RNA, is one of the three major macromolecules that are essential for all known forms of life....
, 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
Chemical bond
A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...
s throughout a nucleic acid with respect to a single coordinate frame. Particularly, RNA molecules are proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
-poor and overlap of ribose
Ribose
Ribose is an organic compound with the formula C5H10O5; specifically, a monosaccharide with linear form H––4–H, which has all the hydroxyl groups on the same side in the Fischer projection....
resonances make it very difficult to use J-coupling
J-coupling
J-coupling is the coupling between two nuclear spins due to the influence of bonding electrons on the magnetic field running between the two nuclei. J-coupling contains information about dihedral angles, which can be estimated using the Karplus equation...
and NOE
Nuclear Overhauser effect
The Nuclear Overhauser Effect is the transfer of nuclear spin polarization from one nuclear spin population to another via cross-relaxation. It is a common phenomenon observed by nuclear magnetic resonance spectroscopy. The theoretical basis for the NOE was described and experimentally verified...
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−3 whereas NOE is proportional to r−6.
RDC measurements have recently been proved useful for a rapid determination of the relative orientations of units of known structures in proteins. 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.
RDC and protein dynamics
Although crystallographicCrystallography
Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...
B-factors and NMR spin relaxation
Relaxation (NMR)
In nuclear magnetic resonance spectroscopy and magnetic resonance imaging the term relaxation describes several processes by which nuclear magnetization prepared in a non-equilibrium state return to the equilibrium distribution. In other words, relaxation describes how fast spins "forget" the...
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. Techniques like quasielastic
Quasielastic scattering
In physics, quasielastic scattering designates a limiting case of inelastic scattering, characterized by energy transfers being small compared to the incident energy of the scattered particles.The term was originally coined in nuclear physics....
and inelastic
Inelastic scattering
In particle physics and chemistry, inelastic scattering is a fundamental scattering process in which the kinetic energy of an incident particle is not conserved . In an inelastic scattering process, some of the energy of the incident particle is lost or gained...
neutron scattering
Neutron scattering
Neutron scattering,the scattering of free neutrons by matter,is a physical processand an experimental technique using this processfor the investigation of materials.Neutron scattering as a physical process is of primordial importance...
, diffuse X-ray scattering, inelastic Mossbauer
Rudolf Mößbauer
Rudolf Ludwig Mössbauer was a German physicist best known for his 1957 discovery of recoilless nuclear resonance fluorescence for which he was awarded the 1961 Nobel Prize in Physics...
scattering and dielectric spectroscopy
Dielectric spectroscopy
Dielectric spectroscopy , and also known as electrochemical impedance spectroscopy, measures the dielectric properties of a medium as a function of frequency...
can in principle provide information about correlated motions. However interpretation of data on molecular level is often difficult. While molecular dynamic simulation
Molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...
are very successful in predicting pico to nano second motions, they are often limited in their abilities in investigating "long"-time scale motions. 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
Dihydrofolate reductase
- Function :Dihydrofolate reductase converts dihydrofolate into tetrahydrofolate, a methyl group shuttle required for the de novo synthesis of purines, thymidylic acid, and certain amino acids...
and cyclophilin
Cyclophilin
Cyclophilins are a family of proteins from vertebrates and other organisms that bind to cyclosporine, an immunosuppressant which is usually used to suppress rejection after internal organ transplants...
A using theoretical techniques. These slow conformational changes have been verified by NMR techniques.
For the first time in 1997, Prestegard et al. investigated slow dynamics (>10−9 s) in myoglobin
Myoglobin
Myoglobin is an iron- and oxygen-binding protein found in the muscle tissue of vertebrates in general and in almost all mammals. It is related to hemoglobin, which is the iron- and oxygen-binding protein in blood, specifically in the red blood cells. The only time myoglobin is found in the...
by RDC measurement. 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°).
Further reading
Books:- Emsley, J. W.; Lindon, J. C. NMR Spectroscopy using liquid crystal solvents; Pergamon Press: Oxford, U.K., 1975.
Review papers:
- Ad Bax and Alexander Grishaev, Current Opinion in Structural Biology, 15:563–570 (2005)
- Rebecca S. Lipsitz and Nico Tjandra, Annu. Rev. Biophys. Biomol. Struct. 33:387–413 (2004)
Classic papers:
- Saupe, A.; Englert, G. Phys. ReV. Lett. 11, 462-464 (1963).
- Saupe, A. Z. Naturforsch. 19a, 161-171 (1964).
- Deloche, B.; Samulski, E. T. Macromolecules 14, 575-581 (1981).
- Nico Tjandra and Ad Bax. Science Vol. 278. no. 5340, pp. 1111 – 1114 (1997)
- Ad Bax et al. Nature Structural Biology 4, 732 - 738 (1997)
- J. R. Tolman et al. Nature Structural Biology 4, 292 - 297 (1997)
- Tjandra, N. & Bax, A., J. Magn. Reson. 124, 512−515 (1997).
- Tjandra, N., Grzesiek, S. & Bax, A., J. Am. Chem. Soc. 118, 6264−6272 (1996).
- Tolman, J.R. & Prestegard, J.H., J. Magn. Reson. B 112, 245−252 (1996).
- Tolman, J.R., Flanagan, J.M., Kennedy, M.A. & Prestegard, J.H., Proc. Natl. Acad. Sci. U.S.A. 92, 9279−9283 (1995).
- Sanders, C.R., Hare, B.J., Howard, K.P. & Prestegard, J.H., Prog. Nucl. Magn. Reson. Spectrosc. 26, 421−444 (1994).
- Bastiaan, E. W., Maclean, C., Van Zijl, P. C. M. & Bothner-By, A. A. Annu. Rep. NMR Spectrosc. 19, 35-77.(1987)
See also
- Residual chemical shift anisotropyResidual chemical shift anisotropyResidual chemical shift anisotropy is the difference between the chemical shift anisotropy of aligned and non-aligned molecules. It is normally three orders of magnitide smaller than static CSA. RCSA is useful for structural determination and it is among the new developments in NMR spectroscopy....
(RCSA) - Solid-state nuclear magnetic resonanceSolid-state nuclear magnetic resonanceSolid-state NMR spectroscopy is a kind of nuclear magnetic resonance spectroscopy, characterized by the presence of anisotropic interactions.-Introduction:Basic concepts...
(ssNMR)