Theory and Applications of Residual Dipolar Couplings in Biomolecular NMR

Theory and Applications of Residual Dipolar Couplings in Biomolecular NMR

Residual Dipolar Couplings (RDC s) Relatively new technique ~ 1996 Nico Tjandra, Ad Bax- NIH, Jim Prestegard, UGA Combination of ideas from solid state NMR, and liquid crystal chemistry NMR (Saupé, early 1960 s) Complementary information for NMR structural determinations, novel information for inter-domain orientation, dynamics and intermolecular complexes

Classical NMR Structure Determination 1980 s Wuthrich s lab, Gerhard Wagner Most NMR structures rely on NOEs NOE- Nuclear Overhauser Effect ( or enhancement) Dipolar interactions between 1 H s Only detectable for 1 H s separated by <6 Å Can be interpreted on in terms of a loosely defined distances between 1 H s, no directional information

NMR Structure Determination Essentially you fold the polypeptide chain to find the best fit to the NOEs

NOE Structures Usually 10-20 NOEs identified per residue, ~60-70% of NOEs are intraresidue or to a neighbouring residue Well determined secondary and tertiary structures of globular domains due to large number of loose constraints Difficult to identify interdomain and intermolecular NOEs: NOE intensity is sensitive to dynamics of nuclei involved

J(spin-spin)-coupling 15 N J N-H =93 Hz 1 H (decoupled) ppm ppm (not decoupled) Only occurs between covalently bonded nuclei (very weak coupling also seen in some H-bonded systems) Independent of dynamics and magnetic field strength

Dipolar Coupling B 0 θ 1 H 15 N In isotropic solution J N-H + ν D = 93Hz (not decoupled) Dipolar coupling- through space interaction, bonded or unbonded ppm ν D = ν (3cos 2 θ-1) /2 ν = (γ H γ N h)/(4π 2 r 3 ) ν Dipolar coupling constant N-H r= 1.02Å, ν = 22,600 Hz H-H r= 3.0 Å, ν = 4,500 Hz

Solid State NMR: dipolar coupling Samples in powders, crystals, membranes etc No motional averaging of dipolar coupling ν D = ν (3cos 2 θ-1)/2 ν D B 0 θ 1 H 15 N -very broad overlapping signals, low signal to noise but directional information Hz

Residual Dipolar Coupling Goal is to get some of the orientational information without the line broadening ν D = ν (3cos 2 θ-1) /2, ν = (γ H γ N h)/(4π 2 r 3 ) J N-H + ν D = 93Hz (not decoupled) ppm J N-H + ν D = 110Hz ppm B 0 -isotropic tumbling: no preferred orientation to B 0 B 0 -anisotropic

Partial Alignment Techniques for Proteins (1) DNA, RNA have large anisotropic magnetic susceptibilities, aromatic ring stacking effects (2) paramagnetic ions bound to proteins also can cause alignment (3) liquid crystal media-molecules with large (unlabeled, NMR invisible) anisotropic magnetic susceptibilities will align with magnetic field and form a liquid crystal:ie phage, bicelles, purple membranes.. (4) mechanical-stretched or compressed polyacrylamide gels

Liquid Crystal Media B 0 -ie: bicelles (a mixture of phospholipids, DMPC(14), DHPC(6)) form disc or puck shaped structures that align with the magnetic field (Sanders, 1992) -interaction of the protein with the liquid crystal is non-specific steric hindrance of some orientations leading to a small fraction in a preferred orientation

Alternate Alignment Methods Phage primarily electrostatic interactions with proteins Gels radial or axial compression, charged or steric interactions

Measuring RDC s Need to orient the protein about 10-3 of the time to get N-H dipolar couplings of ~ 0-±30 Hz, size of ν D can be tuned by varying the concentration of the alignment media J J+ ν D T4 lysozyme

How to convert measured RDC s into structural information Define an arbitrary molecular frame for the protein Relate molecular frame to a molecular alignment tensor to the magnetic field: A A: (3x3) matrix that define direction and degree of alignment relative to B 0 A a :axial component A r :rhombic component S: order parameter r ij : NH bond length

Defining the Alignment Tensor If structure (or preliminary structure) is known and alignment is steric it can be calculated If structure is not known then the alignment tensor can be determined from the distribution of rdc s

(a)bands defined for θ and φ values for an NH vector in ubiquitin relative to the alignment frame (b) no way to tell the difference between A ZZ and -A ZZ

Data Interpretation Once an alignment tensor is defined the RDC s can be interpreted in terms of the angle each bond vector makes with a reference frame Can then be used for data refinement in structure calculations degeneracy can be reduced by using two alignment media

Data Refinement Usually not used in initial refinement steps Once initial NOE structure is calculated, and reasonable fold defined then RDCs can be used to further refine most degenerate orientations can be ruled out by initial fold Calculate RDC based on initial structure E dip =k dip (ν calc - ν meas ) 2 Energy minimize for best fit

RDC refinement improves structures, lower RMSD, more angles in good Ramachandran regions Homology models can be refined using just chemical shift assignments and rdc s -good for structural genomics approaches Ab initio structures have been done but are not common (Hus et al, J. Mol. Biol.298:927,2000)

B 0 Overlay of structure of the CVN protein Red with rdc s Blue without rdc s Small difference Between structures Large difference in quality indicators

Multiple Dipolar Couplings Can define orientation of peptide planes

Orienting Domains Each domain treated separately for initial NOE derived fold and for RDCs Determine the molecular alignment tensor for each domain No translational information, NOE or covalent linker restraints are necessary Wheat germ agglutinin(a) vs BLBC (Biochemistry. 1999 Jul 13;38(28):9013-22.) NMR X-ray

RDC s have a dramatic effect on NMR structures of nucleic acid because of low density of 1 H s and hence few NOEs

Interpretation of Dynamics using RDCs NMR relaxation studies are very useful for identifying the location and rates of dynamic motions in proteins in solution RDC s can also potentially be used to identify the magnitude and orientation of motions Relative orientation of BLBC domains is not constant in solution

Dynamics from RDC s Approaches are still being developed alignment tensor contains information about degree of ordering A generalized degree of order parameter (GDO) can be defined for the a protein or a subset of a protein Ratio of fragment GDO to overall GDO gives an order parameter υ υ, S NH or _, and S CαHα ---

Gaussian Average Fluctuation (GAF) of peptide planes in protein G (Bouvignes et al, PNAS (2005) 102, 13885-13890 ) -millisecond timescale

Summary Dipolar couplings provide a non-short range structural restraint that can be used to improve the quality of globular protein domain structures Dramatically improve the knowledge of interdomain orientation in proteins and nuclei acids Allows new insights into protein dynamics and some knowledge of the types of motions involved Allows accurate docking of intermolecular complexes with minimal NOE input