Solving NMR structures I

--deriving distance restraints from crosspeak intensitiesin 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 tm’s used in an NOESY will be 20-200 ms.

fromGlasel &Deutscherp. 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/r6, 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 tc, 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

-1

0

1

2

3

4

5

6

0 50 100 150 200 250 300

relative crosspeak intensity

mixing time

spin diffusion

direct cross-relaxation

note the delay in buildup

•spin diffusion peaksare usually observedat 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.

class restraint description *for protein w/Mr<20 kDa

strong 1.8-2.7 Å strong intensity in short tm (~50 ms*) NOESY

medium 1.8-3.3 Å weak intensity in short tm (~50 ms*) NOESY

weak 1.8-5.0 Å only 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 choosesan internal standardwhere the maximal nOewill be observed (i.e. something not undergoing a lot of motion)

• this calibration can then be usedto set intensity cutoffs for restraint classes, often using a 1/r6 dependence

tyrosine distancealways the same!

Coupling constants and dihedral angles

• there are relationships between three-bond scalar coupling constants 3J and the corresponding dihedral angles , called Karplus relations:

3J = Acos2 + Bcos + C

fromp. 30Evanstextbook

Empirical Karplus relations in proteins

•comparison of 3J values measured in solution with dihedral angles observed in crystal structures of the same protein allows one to derive empirical Karplus relations:

coupling constantsin solution vs. angles from crystal structure for BPTI

these twoquantitiesdiffer by 60°because they are defined differently from p. 167 Wuthrich textbook

Empirical Karplus relations in proteins

• here are some empirical Karplus relations:

3JH,HN()= 6.4 cos2(- 60°) -1.4 cos(- 60°) + 1.93JH,H2()= 9.5 cos2(- 120°) -1.6 cos(- 120°) + 1.83JH,H3()= 9.5 cos2() -1.6 cos() + 1.83JN,H3()= -4.5 cos2(+ 120°) +1.2 cos(+ 120°) + 0.13JN,H2()= 4.5 cos2(- 120°) +1.2 cos(- 120°) + 0.1

• 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 3JHN-H: 3D HNHA

HN to Hcrosspeak

HN diagonalpeak

this is one plane of a 3D spectrum of ubiquitin. The plane corresponds to this 15N chemical shift

ratio of crosspeakto diagonal intensitiescan be related to 3JHN-H

J small J large

Archer et al. J. Magn. Reson.95, 636 (1991).

3D HNHB

• similar to HNHA but measures 3JN-H couplings

for =180 both 3JN ~1 Hz for =+60,-60 one is ~5, other is ~1

can’t tell the difference unless ’s are stereospecifically assigned

DeMarco, Llinas,& Wuthrich Biopolymers17, p. 2727 (1978).

3D HN(CO)HB experiment

• complementary to HNHB

• measures 3JC,H couplings

Grzesiek et al. J. Magn. Reson. 95,636 (1991).

for a particular b proton,if =180, 3JC,H= ~8 Hzif =+60 or -60, 3JC,H= ~1 Hz

HNHB and HN(CO)HB together

3JC,Hsmall3JC,Hlarge3JN,Hsmall3JN,Hsmall

3JC,Hlarge3JC,Hsmall3JN,Hsmall3JN,Hlarge

3JC,Hsmall3JC,Hsmall3JN,Hlarge3JN,Hsmall

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.

3JH,HN()< 6 Hz = -65° ± 25°3JH,HN()> 8 Hz = -120 ± 40°