Incorporating additional types of information in structure calculation: recent advances chemical shift potentials residual dipolar couplings

Chemical shift potentials structure calculation suites such as X-PLOR and CNS now incorporate the ability to directly refine the structure against chemical shift, based on the ability to accurately calculate chemical shifts from structure. the most commonly used potentials are for 13 C  and 13 C  chemical shifts and 1 H chemical shifts see Clore and Gronenborn, PNAS (1998) 95, 5891.

13 C chemical shift potentials 13 C   and 13 C  chemical shifts are determined largely by the backbone angles  and , so potential energy functions can be used which compare the observed chemical shifts to calculated shifts based on ( ,  ) values in the structure being refined: V Cshift (  ) = K Cshift [(  C  (  )) 2 + (  C  (  )) 2 ] where  C n (  ) 2 = C n expected (  ) - C n observed (  ), n=  or , and K Cshift is a force constant arbitrarily chosen to reflect accuracy of calculated shifts

1 H chemical shift potentials 1 H chemical shifts are a little more complicated to calculate from structure--they depend on more factors however, it has been shown that, given a high resolution crystal structure, the 1 H chemical shifts in solution can be predicted to within ppm using a four term function:  calc =  random +  ring +  E +  ani.  random is a “random coil value”,   ing depends upon proximity and orientation of nearby aromatic rings,   ni is the magnetic anisotropy resulting from backbone and side chain C=O and C-N bonds, and  E is effects due to nearby charged groups.

1 H chemical shift potentials so a 1 H chemical shift potential would have the form V prot = K prot (  calc, i -  obs,i ) 2 summed over all protons in the protein, where K prot is a force constant and  calc, i and  obs,i are calculated and observed shifts for proton i, respectively. a portion of thioredoxin before (blue) and after (red) 1 H chemical shift refinement--some significant differences in the vicinity of W31, which has an aromatic ring that affects nearby chemical shifts

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. 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 short-range structure OK long-range structure bad Zhou et al. Biopolymers ( ) 52, 168. best fit superposition done for this end

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 B 0. 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

the residual dipolar coupling will be related to the angle between the internuclear axis and the direction of the partial ordering. The equations for this are given in Tjandra et al. Nat Struct Biol, 4, 732 (1997), which I will hand out as supplementary reading on Monday. Now suppose we have two different residues in a protein and we are measuring the residual dipolar coupling between the amide nitrogen and amide hydrogen: internuclear axis “axis of partial ordering”: principal axis system of magnetic susceptibility tensor 15 N- 1 H residual dipolar coupling will differ for these two residues. This difference depends on the relative orientation of the two NH groups, but not on the distance between them long-range information!

this picture shows 15 N- 1 H residual dipolar couplings measured in an 15 N- 1 H HSQC spectrum of a protein sample partially oriented using “bicelles” (fragments of lipid bilayer). One of the nice things about residual dipolar couplings is that they are easy to measure. Prestegard et al. Biochemistry (2001) 40, 8677.

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 ( ) 52, 168.

A problem with dipolar couplings is that one cannot distinguish the direction of an internuclear vector from its inverse. Thus the two orientations below give the same dipolar coupling: 15 N-- 1 H 1 H-- 15 N 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. So residual dipolar couplings are especially good for refining models/low resolution structures. Refining initial models with RDCs