Residual dipolar coupling

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The residual dipolar coupling between two spins in a molecule occurs if the molecules in solution exhibit a partial alignment leading to an incomplete averaging of spatially anisotropic dipolar couplings. [1]

Contents

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 useful in biomolecular NMR spectroscopy. [2]

Liquid crystals are commonly used to permit the observation of residual dipolar couplings in high-resolution liquid-state NMR spectra. Shilirren texture.jpg
Liquid crystals are commonly used to permit the observation of residual dipolar couplings in high-resolution liquid-state NMR spectra.

History and pioneering works

NMR spectroscopy in partially oriented media was reported by Alfred Saupe. [3] [4] After this initiation, several NMR spectra in various liquid crystalline phases were reported (see e.g. [5] [6] [7] [8] ).

A second technique for partial alignment that is not limited by a minimum anisotropy is strain-induced alignment in a gel (SAG). [9] The technique was extensively used to study the properties of polymer gels by means of high-resolution deuterium NMR, [10] but only lately gel alignment was used to induce RDCs in molecules dissolved into the gel. [11] [12] 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. [13]

In 1995, NMR spectra were reported for cyanometmyoglobin, which has a very highly anisotropic paramagnetic susceptibility. When taken at very high field, these spectra may contain data that can usefully complement NOEs in determining a tertiary fold. [14]

In 1996 and 1997, the RDCs of a diamagnetic protein ubiquitin were reported. The results were in good agreement with the crystal structures. [15] [16]

Physics

The dipolar coupling between two nuclei depends on the distance between them, and the angle of bond relative to the external magnetic field SSNMR dip coupl vect2.png
The dipolar coupling between two nuclei depends on the distance between them, and the angle of bond relative to the external magnetic field

The secular dipolar coupling Hamiltonian of two spins, and is given by:

where

The above equation can be rewritten in the following form:

where

In isotropic solution molecular tumbling reduces the average value of to zero. We thus observe no dipolar coupling. If the solution is not isotropic then the average value of may be different from zero, and one may observe residual couplings.

RDC can be positive or negative, depending on the range of angles that are sampled. [17]

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: [18]

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.

Measurement

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 susceptibility tensors, Χ. [14]

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 lanthanides).

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. [19] Therefore, many different alignment media have been designed:

NMR experiments

There are numerous methods that have been designed to accurately measure coupling constant between nuclei. [24] 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:

Structural biology

RDC measurement provides information on the global folding 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.

Studies of biomolecular structure

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. RDC and protein structure.png
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.

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-coupling. 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. [25]

RDC target curves for the N-H vector of Asp58 in a tight 10-model ensemble for ubiquitin (PDB:1D3Z) RDC curves on NMRmodels 1d3z D58NH.jpg
RDC target curves for the N-H vector of Asp58 in a tight 10-model ensemble for ubiquitin (PDB:1D3Z)

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 that the specific bond vector makes to the applied magnetic field. [25]

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 bonds 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 also been proved to be extremely useful for a rapid determination of the relative orientations of units of known structures in proteins. [26] [27] 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. [25]

Protein dynamics

As a RDC provides spatially and temporally averaged information about an angle between the external magnetic field and a bond vector in a molecule, it may provide rich geometrical information about dynamics on a slow timescale (>10−9 s) in proteins. In particular, due to its radial dependence the RDC is in particular sensitive to large-amplitude angular processes [28] An early example by Tolman et al. found previously published structures of myoglobin insufficient to explain measured RDC data, and devised a simple model of slow dynamics to remedy this. [29] However, for many classes of proteins, including intrinsically disordered proteins, analysis of RDCs becomes more involved, as defining an alignment frame is not trivial. [30] The problem can be addressed by circumventing the necessity of explicitly defining the alignment frame. [30] [31]

See also

Related Research Articles

The nuclear Overhauser effect (NOE) is the transfer of nuclear spin polarization from one population of spin-active nuclei to another via cross-relaxation. A phenomenological definition of the NOE in nuclear magnetic resonance spectroscopy (NMR) is the change in the integrated intensity of one NMR resonance that occurs when another is saturated by irradiation with an RF field. The change in resonance intensity of a nucleus is a consequence of the nucleus being close in space to those directly affected by the RF perturbation.

In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of an atomic nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of a molecule. Chemical shifts are also used to describe signals in other forms of spectroscopy such as photoemission spectroscopy.

<span class="mw-page-title-main">Nuclear magnetic resonance spectroscopy</span> Laboratory technique

Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique based on re-orientation of atomic nuclei with non-zero nuclear spins in an external magnetic field. This re-orientation occurs with absorption of electromagnetic radiation in the radio frequency region from roughly 4 to 900 MHz, which depends on the isotopic nature of the nucleus and increased proportionally to the strength of the external magnetic field. Notably, the resonance frequency of each NMR-active nucleus depends on its chemical environment. As a result, NMR spectra provide information about individual functional groups present in the sample, as well as about connections between nearby nuclei in the same molecule. As the NMR spectra are unique or highly characteristic to individual compounds and functional groups, NMR spectroscopy is one of the most important methods to identify molecular structures, particularly of organic compounds.

<span class="mw-page-title-main">Magic angle spinning</span>

In solid-state NMR spectroscopy, magic-angle spinning (MAS) is a technique routinely used to produce better resolution NMR spectra. MAS NMR consists in spinning the sample at the magic angle θm with respect to the direction of the magnetic field.

<span class="mw-page-title-main">Electron paramagnetic resonance</span> Technique to study materials that have unpaired electrons

Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials that have unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but the spins excited are those of the electrons instead of the atomic nuclei. EPR spectroscopy is particularly useful for studying metal complexes and organic radicals. EPR was first observed in Kazan State University by Soviet physicist Yevgeny Zavoisky in 1944, and was developed independently at the same time by Brebis Bleaney at the University of Oxford.

<span class="mw-page-title-main">Solid-state nuclear magnetic resonance</span>

Solid-state NMR (ssNMR) spectroscopy is a technique for characterizing atomic level structure in solid materials e.g. powders, single crystals and amorphous samples and tissues using nuclear magnetic resonance (NMR) spectroscopy. The anisotropic part of many spin interactions are present in solid-state NMR, unlike in solution-state NMR where rapid tumbling motion averages out many of the spin interactions. As a result, solid-state NMR spectra are characterised by larger linewidths than in solution state NMR, which can be utilized to give quantitative information on the molecular structure, conformation and dynamics of the material. Solid-state NMR is often combined with magic angle spinning to remove anisotropic interactions and improve the resolution as well as the sensitivity of the technique.

The magic angle is a precisely defined angle, the value of which is approximately 54.7356°. The magic angle is a root of a second-order Legendre polynomial, P2(cos θ) = 0, and so any interaction which depends on this second-order Legendre polynomial vanishes at the magic angle. This property makes the magic angle of particular importance in magic angle spinning solid-state NMR spectroscopy. In magnetic resonance imaging, structures with ordered collagen, such as tendons and ligaments, oriented at the magic angle may appear hyperintense in some sequences; this is called the magic angle artifact or effect.

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, and also nucleic acids, and their complexes. The field was pioneered by Richard R. Ernst and Kurt Wüthrich at the ETH, and by Ad Bax, Marius Clore, Angela Gronenborn at the NIH, and Gerhard Wagner at Harvard University, among others. Structure determination by NMR spectroscopy usually consists of several phases, each using a separate set of highly specialized techniques. The sample is prepared, measurements are made, interpretive approaches are applied, and a structure is calculated and validated.

In nuclear chemistry and nuclear physics, J-couplings are mediated through chemical bonds connecting two spins. It is an indirect interaction between two nuclear spins that arises from hyperfine interactions between the nuclei and local electrons. In NMR spectroscopy, J-coupling contains information about relative bond distances and angles. Most importantly, J-coupling provides information on the connectivity of chemical bonds. It is responsible for the often complex splitting of resonance lines in the NMR spectra of fairly simple molecules.

Magnetic dipole–dipole interaction, also called dipolar coupling, refers to the direct interaction between two magnetic dipoles. Roughly speaking, the magnetic field of a dipole goes as the inverse cube of the distance, and the force of its magnetic field on another dipole goes as the first derivative of the magnetic field. It follows that the dipole-dipole interaction goes as the inverse fourth power of the distance.

Residual chemical shift anisotropy (RCSA) is the difference between the chemical shift anisotropy (CSA) of aligned and non-aligned molecules. It is normally three orders of magnitude smaller than the static CSA, with values on the order of parts-per-billion (ppb). RCSA is useful for structural determination and it is among the new developments in NMR spectroscopy.

Adriaan "Ad" Bax is a Dutch-American molecular biophysicist. He was born in the Netherlands and is the Chief of the Section on Biophysical NMR Spectroscopy at the National Institutes of Health. He is known for his work on the methodology of biomolecular NMR spectroscopy. He is a corresponding member of the Royal Netherlands Academy of Arts and Sciences, a member of the National Academy of Sciences, a fellow of the American Academy of Arts and Sciences, and a Foreign Member of the Royal Society.

<span class="mw-page-title-main">Nuclear magnetic resonance</span> Spectroscopic technique based on change of nuclear spin state

Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. Nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics and crystals as well as non-crystalline materials. NMR is also routinely used in advanced medical imaging techniques, such as in magnetic resonance imaging (MRI). The original application of NMR to condensed matter physics is nowadays mostly devoted to strongly correlated electron systems. It reveals large many-body couplings by fast broadband detection and it should not to be confused with solid state NMR, which aims at removing the effect of the same couplings by Magic Angle Spinning techniques.

Nuclear magnetic resonance crystallography is a method which utilizes primarily NMR spectroscopy to determine the structure of solid materials on the atomic scale. Thus, solid-state NMR spectroscopy would be used primarily, possibly supplemented by quantum chemistry calculations, powder diffraction etc. If suitable crystals can be grown, any crystallographic method would generally be preferred to determine the crystal structure comprising in case of organic compounds the molecular structures and molecular packing. The main interest in NMR crystallography is in microcrystalline materials which are amenable to this method but not to X-ray, neutron and electron diffraction. This is largely because interactions of comparably short range are measured in NMR crystallography.

Nucleic acid NMR is the use of nuclear magnetic resonance spectroscopy to obtain information about the structure and dynamics of nucleic acid molecules, such as DNA or RNA. It is useful for molecules of up to 100 nucleotides, and as of 2003, nearly half of all known RNA structures had been determined by NMR spectroscopy.

CS-ROSETTA is a framework for structure calculation of biological macromolecules on the basis of conformational information from NMR, which is built on top of the biomolecular modeling and design software called ROSETTA. The name CS-ROSETTA for this branch of ROSETTA stems from its origin in combining NMR chemical shift (CS) data with ROSETTA structure prediction protocols. The software package was later extended to include additional NMR conformational parameters, such as Residual Dipolar Couplings (RDC), NOE distance restraints, pseudocontact chemical shifts (PCS) and restraints derived from homologous proteins. This software can be used together with other molecular modeling protocols, such as docking to model protein oligomers. In addition, CS-ROSETTA can be combined with chemical shift resonance assignment algorithms to create a fully automated NMR structure determination pipeline. The CS-ROSETTA software is freely available for academic use and can be licensed for commercial use. A software manual and tutorials are provided on the supporting website https://csrosetta.chemistry.ucsc.edu/.

<span class="mw-page-title-main">Conformational ensembles</span> Computational models of intrinsically-disordered proteins

In computational chemistry, conformational ensembles, also known as structural ensembles, are experimentally constrained computational models describing the structure of intrinsically unstructured proteins. Such proteins are flexible in nature, lacking a stable tertiary structure, and therefore cannot be described with a single structural representation. The techniques of ensemble calculation are relatively new on the field of structural biology, and are still facing certain limitations that need to be addressed before it will become comparable to classical structural description methods such as biological macromolecular crystallography.

The Biological Magnetic Resonance Data Bank is an open access repository of nuclear magnetic resonance (NMR) spectroscopic data from peptides, proteins, nucleic acids and other biologically relevant molecules. The database is operated by the University of Wisconsin–Madison and is supported by the National Library of Medicine. The BMRB is part of the Research Collaboratory for Structural Bioinformatics and, since 2006, it is a partner in the Worldwide Protein Data Bank (wwPDB). The repository accepts NMR spectral data from laboratories around the world and, once the data is validated, it is available online at the BMRB website. The database has also an ftp site, where data can be downloaded in the bulk. The BMRB has two mirror sites, one at the Protein Database Japan (PDBj) at Osaka University and one at the Magnetic Resonance Research Center (CERM) at the University of Florence in Italy. The site at Japan accepts and processes data depositions.

<span class="mw-page-title-main">James J. Chou</span> American chemist

James J. Chou (周界文) is a Chinese American scientist and Professor of Biological Chemistry and Molecular Pharmacology at the Harvard Medical School. He is known for pioneering the use of Nuclear Magnetic Resonance (NMR) Spectroscopy to reveal the structural details of the membrane regions of cell surface proteins, particularly those of immune receptors and viral membrane proteins.

<span class="mw-page-title-main">Spinach (software)</span> Magnetic resonance simulation package

Spinach is an open-source magnetic resonance simulation package initially released in 2011 and continuously updated since. The package is written in Matlab and makes use of the built-in parallel computing and GPU interfaces of Matlab.

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