Sign-in   Home    Members    Sitemap    Statistics    About    Contact-us    FAQ    Feedback

nmr 2.0 Blog

Archive for the ‘Residual Dipolar Couplings’ Category

Residual Dipolar Coupling

without comments

Depiction of interaction between a protein and bicelle at the interface.

Figure 1. Depiction of interaction between a protein and bicelle at their interface.

Residual dipolar couplings (RDCs) had been observed as early as 1963 [1] in nematic environments. A number of recent applications [2-7] have reignited their wide use in application to a broad spectrum of biomolecules. RDCs have been used in studies of carbohydrates [8-10], nucleic acids [11-13] and proteins [14-16] to mention a few. Residual dipolar couplings can be acquired very rapidly and accurately by a number of techniques including direct measurement of splittings in coupled heteronuclear single quantum coherence spectra (HSQC) [17-19] and provide simultaneous structural [4;15;20] and motional [5;7;13;21-23] information.
RDCs arise from the interaction of two magnetically active nuclei in the presence of the external magnetic field of a NMR instrument [3;4]. This interaction is normally reduced to zero due to the isotropic tumbling of molecules in their aqueous environment. The introduction of a partial order to the molecular alignment by minutely limiting their isotropic tumbling will resurrect the RDC observable. This partial order can be introduced by either magnetic anisotropy of the molecule [3], a crystalline aqueous solution [24] as illustrated in Figure1 or incorporation of artificial tags with magnetic anisotropy susceptibility such as Lanthanide [25]. Equation 1 describes the time average observable of the RDC interaction between a pair of spin ½ nuclei.

D_{ij}=-\left(\frac{\mu_{o}\gamma_{i}\gamma_{j}h}{(2\pi r)^{3}}\right)\left\langle \frac{3\cos^{2}(\theta_{ij})-1}{2}\right\rangle    (1)

Here, Dij denotes the residual dipolar coupling in units of Hz between nuclei i and j, γi and γj are nuclear magnetogyric ratios, rij is the internuclear distance (assumed fixed for directly bonded atoms) and θij(t) is the time dependent angle of the internuclear vector with respect to the external magnetic field. The angle brackets signify the time average of the quantity.
Simple algebraic manipulation of equation 1 produces the more familiar formulation of RDC interaction shown in Equation 2.

D_{\mathit{ij}}=D_{\mathit{max}}\underset{k,l}{\sum}{s_{\mathit{kl}}\cos \theta _{k}^{\mathit{ij}}\cos \theta_{l}^{\mathit{ij}}} (2)
The indexes k and l in Eq 2 denote the orthonormal basis sets that span the Cartesian space  (\hat{i}, \hat{j}, \hat{k}) and D_{\mathit{max}}=-{\mu _{0}\gamma _{i}\gamma _{j}h}/{(2\pi r)^{3}}. Entities skl in this equation represent various components of anisotropy, are referred to as the elements of the Saupe order tensor matrix, and are defined by Eq 3. Note that the entities \cos \theta_{k}^{\mathit{ij}} represent the direction cosine of the vector connecting nuclei i and j to the k-th axis of the molecular frame. Equation 4 illustrates a more familiar form of this equation after expansion of the two embedded summations in Eq 2.
s_{\mathit{kl}}=\left\langle \frac{3\cos \left(\theta _{k}\right)\cos\left(\theta _{l}\right)-\delta _{\mathit{kl}}}{2}\right\rangle (3)

D_{\mathit{ij}}=D_{\mathit{max}}\left(\cos ^{2}\theta_{x}^{\mathit{ij}}s_{\mathit{xx}}+\cos ^{2}\theta_{y}^{\mathit{ij}}s_{\mathit{yy}}+\cos ^{2}\theta_{z}^{\mathit{ij}}s_{\mathit{zz}}+2\cos \theta _{x}^{\mathit{ij}}\cos\theta _{y}^{\mathit{ij}}s_{\mathit{xy}}+2\cos \theta_{x}^{\mathit{ij}}\cos \theta _{z}^{\mathit{ij}}s_{\mathit{xz}}+2\cos\theta _{y}^{\mathit{ij}}\cos \theta_{z}^{\mathit{ij}}s_{\mathit{yz}}\right) (4)

Bibliography

[1] Saupe, A & Englert, G. Phys. rev. lett;high-resolution nuclear magnetic resonance spectra of orientated molecules. Phys. Rev. Lett (1963) 11: pp. 462-464.

[2] Zhou, H J, Vermeulen, A, Jucker, F M & Pardi, A. Biopolymers;incorporating residual dipolar couplings into the nmr solution structure determination of nucleic acids. Biopolymers (1999) 52: pp. 168-180.

[3] Prestegard JH AH&TJ. Nmr structures of biomolecules using field oriented media and residual dipolar couplings. Q. Rev. Biophys. (2000) 33: p. pp. 371-424.

[4] Bax A, Kontaxis G & Tjandra N. Dipolar couplings in macromolecular structure determination. In Nuclear Magnetic Resonance of Biological Macromolecules, Pt B. . 2001. p. pp. 127-174.

[5] Tolman JR. Dipolar couplings as a probe of molecular dynamics and structure in solution. Curr. Opin. Struct. Biol. (2001) 11: pp. 532-539.

[6] de Alba, E & Tjandra, N. Progress in nuclear magnetic resonance spectroscopy;nmr dipolar couplings for the structure determination of biopolymers in solution. Progress in Nuclear Magnetic Resonance Spectroscopy (2002) 40: pp. 175-197.

[7] Blackledge M. Recent progress in the study of biomolecular structure and dynamics in solution from residual dipolar couplings. Progress in Nuclear Magnetic Resonance Spectroscopy (2005) 46: pp. 23-61.

[8] Azurmendi HF, Martin-Pastor M & Bush CA. Conformational studies of lewis x and lewis a trisaccharides using nmr residual dipolar couplings. Biopolymers (2002) 63: pp. 89-98.

[9] Azurmendi HF & Bush CA. Conformational studies of blood group a and blood group b oligosaccharides using nmr residual dipolar couplings. Carbohydr. Res. (2002) 337: p. pp. 905-915.

[10] Tian F, Al-Hashimi HM, Craighead JL & Prestegard JH. Conformational analysis of a flexible oligosaccharide using residual dipolar couplings. J. Am. Chem. Soc. (2001) 123: p. pp. 485-492.

[11] Tjandra N, Tate S, Ono A, Kainosho M & Bax A. The nmr structure of a dna dodecamer in an aqueous dilute liquid crystalline phase. J. Am. Chem. Soc. (2000) 122: p. pp. 6190-6200.

[12] Vermeulen, A, Zhou, H J & Pardi, A. ;determining dna global structure and dna bending by application of nmr residual dipolar couplings. J. Am. Chem. Soc. (2000) 122: pp. 9638-9647.

[13] Al-Hashimi HM, Gosser Y, Gorin A, Hu WD, Majumdar A & Patel DJ. Concerted motions in hiv-1 tar rna may allow access to bound state conformations: rna dynamics from nmr residual dipolar couplings. J. Mol. Biol. (2002) 315: p. pp. 95-102.

[14] Tian F, Valafar H & Prestegard JH. A dipolar coupling based strategy for simultaneous resonance assignment and structure determination of protein backbones. J. Am. Chem. Soc. (2001) 123: pp. 11791-11796.

[15] Cornilescu G, Delaglio F & Bax A. Protein backbone angle restraints from searching a database for chemical shift and sequence homology. J. Biomol. NMR (1999) 13: pp. 289-302.

[16] Clore GM & Bewley CA. Using conjoined rigid body/torsion angle simulated annealing to determine the relative orientation of covalently linked protein domains from dipolar couplings. Journal of Magnetic Resonance (2002) 154: p. pp. 329-335.

[17] Bodenhausen, G & Ruben, DJ. Chemical physics letters;natural abundance n-15 nmr by enhanced heteronuclear spectroscopy. Chemical Physics Letters (1980) 69: pp. 185-189.

[18] Bax, A, Vuister, G W, Grzesiek, S, Delaglio, F, Wang, A C, Tschudin, R & Zhu, G. Measurement of homonuclear and heteronuclear j-couplings from quantitative j-correlation. In Nuclear Magnetic Resonance, Pt C. . 1994. p. pp. 79-105.

[19] Tolman, J R & Prestegard, JH. Journal of magnetic resonance series b;measurement of amide n-15-h-1 one-bond couplings in proteins using accordion heteronuclear-shift-correlation experiments. Journal of Magnetic Resonance Series B (1996) 112: pp. 269-274.

[20] Delaglio F, Kontaxis G & Bax A. Protein structure determination using molecular fragment replacement and nmr dipolar couplings. J. Am. Chem. Soc. (2000) 122: pp. 2142-2143.

[21] Bernado P & Blackledge M. Local dynamic amplitudes on the protein backbone from dipolar couplings: toward the elucidation of slower motions in biomolecules. J. Am. Chem. Soc. (2004) 126: pp. 7760-7761.

[22] Al-Hashimi HM, Gosser Y, Gorin A, Hu WD, Majumdar A & Patel DJ. Concerted motions in hiv-1 tar rna may allow access to bound state conformations: rna dynamics from nmr residual dipolar couplings. J. Mol. Biol. (2002) 315: pp. 95-102.

[23] Yi X, Venot A, Glushka J & Prestegard JH. Glycosidic torsional motions in a bicelle-associated disaccharide from residual dipolar couplings. J. Am. Chem. Soc. (2004) 126: pp. 13636-13638.

[24] Bax A. Weak alignment offers new nmr opportunities to study protein structure and dynamics. Protein Science (2003) 12: pp. 1-16.

[25] Prestegard JH, al-Hashimi HM & Tolman JR. Nmr structures of biomolecules using field oriented media and residual dipolar couplings. Q. Rev. Biophys. (2000) 33: pp. 371-424.

[26] Prestegard JH & Kishore A. Current opinion in structural biology;partial alignment of biomolecules: an aid to nmr characterization. Curr. Opin. Struct. Biol. (2001) 5: pp. 584-590.

[27] Nitz M, Sherawat M, Franz KJ, Peisach E, Allen KN & Imperiali B. Structural origin of the high affinity of a chemically evolved lanthanide-binding peptide. Angewandte Chemie-International Edition (2004) 43: pp. 3682-3685.

[28] Valafar, H. & Prestegard, J.H.. Redcat: a residual dipolar coupling analysis tool. J. Magn. Reson. (2004) 167: p. p. p. 228-41..

[29] Losonczi J, Andrec M, Fischer M & Prestegard J. Order matrix analysis of residual dipolar couplings using singular value decomposition. Journal of Magnetic Resonance (1999) 138: pp. 334-342.

[30] Bryson M, Tian F, Prestegard JH & Valafar H. Redcraft: a tool for simultaneous characterization of protein backbone structure and motion from rdc data. J. Magn. Reson. (2008) 191: pp. 322-334.

[31] Miao X, Mukhopadhyay R & Valafar H. Estimation of relative order tensors, and reconstruction of vectors in space using unassigned rdc data and its application. Journal of Magnetic Resonance (2008) 194: pp. 202-211.

Share

Written by homayoun

October 9th, 2009 at 1:37 pm