Residual dipolar couplings in NMR structure determination Bioc 585, Feb 26, 2008

Long-range information in NMR a traditional weakness of NMR is that all the structural restraints are short-range in nature (meaning short-range in terms of distance, not in terms of the sequence), i.e. nOe restraints are only between atoms <5 Å apart, dihedral angle restraints only restrict groups of atoms separated by three bonds or fewer over large distances, uncertainties in short-range restraints will add up--this means that NMR structures of large, elongated systems (such as B-form DNA, for instance) will be poor overall even though individual regions of the structure will be well-defined. long-range structure bad to illustrate this point, in the picture at left, simulated nOe restraints were generated from the red DNA structure and then used to calculate the ensemble of black structures best fit superposition done for this end short-range structure OK Zhou et al. Biopolymers (1999-2000) 52, 168.

Residual dipolar couplings recall that the spin dipolar coupling depends on the distance between 2 spins, and also on their orientation with respect to the static magnetic field B0. In solution, the orientational term averages to zero as the molecule tumbles, so that splittings in resonance lines are not observed--i.e. we can’t measure dipolar couplings. This is too bad, in a way, because this orientational term carries structural info, as we’ll see In solids, on the other hand, the couplings don’t average to zero, but they are huge, on the order of the width of a whole protein spectrum. This is too big to be of practical use in high-resolution protein work compromise: it turns out that you can use various kinds of media, from liquid crystals to phage, to partially orient samples, so that the dipolar coupling no longer averages to zero but has some small residual value

Residual dipolar couplings: A Goldilocks tale B0 B0 Proteins in a single crystal Complete orientational bias Enormous dipolar coupling. Too big! (Dipolar couplings as big as entire proton spectral range) Proteins tumbling isotropically in solution No orientational bias Dipolar interaction averages to zero with tumbling No observable dipolar coupling. Too small!

...but the third bowl of porridge was just right. filamentous phage, lipid bilayer fragment, cellulose crystallite Proteins dissolved in liquid but oriented medium Some liquid crystals acquire macroscopic order in a magnetic field e.g. bicelles, filamentous phage, cellulose crystallites Collisions w/protein impart a slight orientational bias A small “residual dipolar coupling” results Just right! --> gives interpretable information

Measurement of Residual Dipolar Couplings --regular HSQC --decoupled in both dimensions --15N-1H splittings not observed --HSQC without decoupling in 15N dimension -- isotropic solution --15N-1H splittings observed, equal to 15N-1H one-bond scalar coupling (~92-95 Hz) --HSQC without decoupling in 15N dimension --partly oriented --15N-1H splittings observed, equal to 15N-1H one-bond scalar coupling plus RDC! Some RDC -, some +

RDCs can often be “tuned” by adjusting the composition of the liquid Prestegard et al. Biochemistry (2001) 40, 8677. This picture illustrates measurement of 15N-1H residual dipolar couplings for a protein in a 7% bicelle (fragments of lipid bilayer) solution. The bicelle preparation is isotropic (not ordered) at 25 °C (left), allowing measurement of the scalar couplings. Upon heating to 35 °C, the bicelle preparation becomes anisotropic (ordered) such that the measured coupling now includes an RDC component. RDCs can therefore be measured by comparing spectra taken at the different temperatures. RDCs can often be “tuned” by adjusting the composition of the liquid crystal mixture.

SAG: Strain induced alignment in a gel pores in gel contain protein axially compressed, radially stretched oblate ellipsoid pores radially compressed, axially stretched prolate ellipsoid pores regular polyacrylamide gel Proteins can be incorporated into cylindrical polyacrylamide gels within NMR tubes. If the gel is stretched or compressed, the pores become anisotropic and can impart partial order to a protein just like a liquid crystal can.

Interpretation of RDCs--what do they mean? Recall that the spin dipolar interaction between two nuclei depends upon their relative position with respect to an external magnetic field. The residual dipolar coupling will therefore be related to the angle between the internuclear axis and the direction of the partial ordering of the protein. See Tjandra et al. Nat Struct Biol, 4, 732 (1997) for a more thorough treatment. Because the internuclear axis will have a different orientation for different bonds in the protein, the RDCs will exhibit a broad range of values. internuclear axis (bond vector) “axis of partial ordering”: principal axis system of magnetic susceptibility tensor 15N-1H residual dipolar coupling will differ for these two residues.

RDCs give information about long-range order in proteins Note that the relative values of 15N-1H RDCs for a set of amide nitrogen hydrogen pairs do not depend upon the distance between those pairs, only on their relative orientation with respect to a common axis system! 15N 1H 15N 1H 15N 15N 1H 1H two NH bond vectors close together two NH bond vectors far apart, but with same orientation In other words, RDCs can in principle tell us the relative orientation of two bond vectors even if they are on opposite ends of the molecule. Contrast this with NOE distance restraints and dihedral angle restraints which define short range order.

Most measured RDCs are one-bond couplings Recall that the spin dipolar interaction, and therefore the RDC, has both a steep distance dependence and an orientational dependence. If we are considering a particular type of RDC, say a one-bond coupling between amide hydrogens and amide nitrogens, the interatomic distances are all the same and equal to an NH bond length. The RDC depends only on the orientational component. This would also still be true for a two-bond RDC, but for a three-bond RDC the distance would vary with the dihedral angle, making interpretation less straightforward. Most measured RDCs are “one-bond”, e.g. between an amide proton and its directly attached nitrogen, since these correspond to distances less than < 1.5 Å generally. However, you’ll notice in the Chou paper that they measure five dipolar couplings per residue, including HN, HC, CC and CN one-bond couplings, but also including the 1Ha-13C’ two-bond coupling (C’ means the carbonyl carbon). So two-bond RDCs are not unheard of.

Illustration of effect of using residual dipolar couplings on the quality of nucleic acid structure determination by NMR a) without rdc b) with rdc Zhou et al. Biopolymers (1999-2000) 52, 168.

Refining initial models with RDCs A problem with dipolar couplings is that one cannot distinguish the direction of an internuclear vector from its inverse. Thus the two opposite orientations below give the same RDC value: 15N--1H 1H--15N This ambiguity makes calculating a structure de novo (i.e. from a random starting model) using only residual dipolar couplings very computationally difficult. If there is a reasonable starting model, however, this is not a problem. Thus residual dipolar couplings are especially good for refining models/low resolution structures.