Solving NMR structures I --deriving distance restraints from crosspeak intensities in NOESY spectra --deriving dihedral angle restraints from J couplings; measuring J couplings

Using NOESY to generate nOe distance restraints NOESY measurements are not steady-state nOe’s: we are not saturating one resonance with constant irradiation while observing the effects at another. Instead, we are pulsing all of the resonances, and then allowing nOe’s to build up through cross-relaxation during a mixing time - -so nOe’s in a NOESY are kinetic: crosspeak intensities will vary with mixing time typical t m ’s used in an NOESY will be ms. from Glasel & Deutscher p. 354 basic NOESY pulse sequence mixing time

nOe buildup in NOESY other things being equal, the initial rate of buildup of a NOESY crosspeak is proportional to 1/r 6, where r is the distance between the two nuclei undergoing cross- relaxation. nOe buildup will be faster for larger proteins, which have a longer correlation time t c, and therefore more efficient zero- quantum cross-relaxation initially crosspeak intensity builds up linearly with time, but then levels off, and at very long mixing time will actually start to drop due to direct (not cross) relaxation.

spin diffusion under certain circumstances, indirect cross-relaxation pathways can be more efficient than direct ones, i.e. A to B to C more efficient than A to C. This is called spin diffusion when this happens the crosspeak intensity may not be a faithful reflection of the distance between the two nuclei.

Crosspeaks due to spin diffusion exhibit delayed buildup in NOESY experiments spin diffusion peaks are usually observed at long mixing time, and their intensity does not reflect the initial rate of buildup these effects can be avoided either by sticking with short mixing times or by examining buildup curves over a range of mixing times

Other nOe caveats I mentioned that nOe buildup rates are faster for larger proteins because of the longer correlation time It’s also true that buildup rates can differ for nuclei within the same protein if different parts of the protein have different mobility (hence different correlation times) for parts of the protein which are relatively rigid (such as the hydrophobic core) correlation times will more or less reflect that of the whole protein molecule--nOe buildup will be fast disordered regions (at the N- or C-termini, for instance) may have much shorter effective correlation times and much slower nOe buildup as a consequence the bottom line is, the actual nOe observed between two nuclei at a given distance r is often less than that expected on the basis of the overall molecular correlation time.

The goal: translating NOESY crosspeak intensities into nOe distance restraints because the nOe is not always a faithful reflection of the internuclear distance, one does not, in general, precisely translate intensities into distances! instead, one usually creates three or four restraint classes which match a range of crosspeak intensities to a range of possible distances, e.g. classrestraintdescription*for protein w/M r <20 kDa strong Åstrong intensity in short t m (~50 ms*) NOESY medium Åweak intensity in short t m (~50 ms*) NOESY weak Åonly visible in longer mixing time NOESY notice that the lower bound of 1.8 Å (approximately van der Waals contact) is the same in all restraint classes. This is because, for reasons stated earlier, atoms that are very close can nonetheless have very weak nOe’s, or even no visible crosspeak at all.

Calibration of nOe’s the crosspeak intensities are often calibrated against the crosspeak intensity of some internal standard where the internuclear distance is known. The idea of this is to figure out what the maximal nOe observable will be for a given distance. ideally, one chooses an internal standard where the maximal nOe will be observed (i.e. something not undergoing a lot of motion) this calibration can then be used to set intensity cutoffs for restraint classes, often using a 1/r 6 dependence tyrosine  distance always the same!

Coupling constants and dihedral angles there are relationships between three-bond scalar coupling constants 3 J and the corresponding dihedral angles , called Karplus relations: 3 J = Acos 2  + Bcos  + C from p. 30 Evans textbook

Empirical Karplus relations in proteins comparison of 3 J values measured in solution with dihedral angles observed in crystal structures of the same protein allows one to derive empirical Karplus relations: coupling constants in solution vs.  angles from crystal structure for BPTI these two quantities differ by 60° because they are defined differently from p. 167 Wuthrich textbook

Empirical Karplus relations in proteins here are some empirical Karplus relations: 3 J H ,HN (  )= 6.4 cos 2 (  - 60°) -1.4 cos(  - 60°) J H ,H  2 (   )= 9.5 cos 2 (    - 120°) -1.6 cos(    - 120°) J H ,H  3 (   )= 9.5 cos 2 (   ) -1.6 cos(   ) J N,H  3 (   )= -4.5 cos 2 (    + 120°) +1.2 cos(    + 120°) J N,H  2 (   )= 4.5 cos 2 (    - 120°) +1.2 cos(    - 120°) notice that use of the relations involving the  hydrogens would require that they be stereospecifically assigned (in cases where there are two  hydrogens) note that these relations involve  or  1 angles

Measuring 3 J HN-H  : 3D HNHA HN to H  crosspeak HN diagonal peak this is one plane of a 3D spectrum of ubiquitin. The plane corresponds to this 15 N chemical shift ratio of crosspeak to diagonal intensities can be related to 3 J HN-H  J small J large Archer et al. J. Magn. Reson. 95, 636 (1991).

3D HNHB similar to HNHA but measures 3 J N-H  couplings for   =180 both 3 J N  ~1 Hz for   =+60,-60 one is ~5, other is ~1 can’t tell the difference unless  ’s are stereospecifically assigned DeMarco, Llinas, & Wuthrich Biopolymers 17, p (1978).

3D HN(CO)HB experiment complementary to HNHB measures 3 J C,H  couplings Grzesiek et al. J. Magn. Reson. 95, 636 (1991). for a particular b proton, if  =180, 3 J C,H  = ~8 Hz if  =+60 or -60, 3 J C,H  = ~1 Hz

HNHB and HN(CO)HB together 3 J C,H   small 3 J C,H   large 3 J N,H   small 3 J N,H   small 3 J C,H   large 3 J C,H   small 3 J N,H   small 3 J N,H   large 3 J C,H   small 3 J C,H   small 3 J N,H   large 3 J N,H   small

HNHB, HN(CO)HB together can thus get both  1 angle and stereospecific assignments for  ’s from a combination of HNHB and HN(CO)HB HNHB HN(CO)HB from Bax et al. Meth. Enzym. 239, 79.

Dihedral angle restraints derived from measured J couplings as with nOe’s, one does not translate J directly into a quantitative dihedral angle, rather one translates a range of J into a range of possible angles, e.g. 3 J H ,HN (  )< 6 Hz  = -65° ± 25° 3 J H ,HN (  )> 8 Hz  = -120 ± 40°