Solving NMR structures I

1
Solving NMR structures I
--deriving distance restraints from crosspeak
intensities in NOESY spectra --deriving dihedral
angle restraints from J couplings measuring J
couplings
2
Using NOESY to generate nOe distance restraints

• NOESY measurements are not steady-state nOes 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 nOes to build up through
  cross-relaxation during a mixing time --so nOes
  in a NOESY are kinetic crosspeak intensities
  will vary with mixing time
• typical tms used in an NOESY will be 20-200 ms.

from Glasel Deutscher p. 354
mixing time
basic NOESY pulse sequence
3
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.

4
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.

5
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

6
Other nOe caveats

• I mentioned that nOe buildup rates are faster for
  larger proteins because of the longer correlation
  time
• Its 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.

7
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/Mrlt20
  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 nOes, or even no
  visible crosspeak at all.

8
Calibration of nOes

• 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.

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

tyrosine d-e distance always the same!

• ideally, one chooses
• an internal standard
• where the maximal nOe
• will be observed (i.e. something not undergoing a
  lot of motion)

9
Coupling constants and dihedral angles

• there are relationships between three-bond scalar
  coupling constants 3J and the corresponding
  dihedral angles q, called Karplus relations
• 3J Acos2q Bcosq C

from p. 30 Evans textbook
10
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 constants in solution vs. f angles from
crystal structure for BPTI
these two quantities differ by 60 because they
are defined differently
from p. 167 Wuthrich textbook
11
Empirical Karplus relations in proteins

• here are some empirical Karplus relations
• 3JHa,HN(f) 6.4 cos2(f - 60) -1.4 cos(f - 60)
  1.9
• 3JHa,Hb2(c1) 9.5 cos2(c1 - 120) -1.6 cos(c1 -
  120) 1.8
• 3JHa,Hb3(c1) 9.5 cos2(c1) -1.6 cos(c1) 1.8
• 3JN,Hb3(c1) -4.5 cos2(c1 120) 1.2 cos(c1
  120) 0.1
• 3JN,Hb2(c1) 4.5 cos2(c1 - 120) 1.2 cos(c1 -
  120) 0.1
• notice that use of the relations involving the b
  hydrogens would require that they be
  stereospecifically assigned (in cases where there
  are two b hydrogens)

12
Measuring 3JHN-Ha 3D HNHA
ratio of crosspeak to diagonal intensities can be
related to 3JHN-Ha
J large
J small
HN to Ha crosspeak
HN diagonal peak
this is one plane of a 3D spectrum of ubiquitin.
The plane corresponds to this 15N chemical shift
Archer et al. J. Magn. Reson. 95, 636 (1991).
13
3D HNHB

• similar to HNHA but measures 3JN-Hb couplings

DeMarco, Llinas, Wuthrich Biopolymers 17, p.
2727 (1978).
for c1 180 both 3JNb 1 Hz for c1 60,-60 one
is 5, other is 1 cant tell the difference
unless bs are stereospecifically assigned
14
3D HN(CO)HB experiment

• complementary to HNHB
• measures 3JC,Hb couplings

for a particular b proton, if q180, 3JC,Hb 8
Hz if q60 or -60, 3JC,Hb 1 Hz
Grzesiek et al. J. Magn. Reson. 95, 636 (1991).
15
HNHB and HN(CO)HB together
3JC,Hb3 small 3JC,Hb2 large 3JN,Hb3
small 3JN,Hb2 small
3JC,Hb3 large 3JC,Hb2 small 3JN,Hb3
small 3JN,Hb2 large
3JC,Hb3 small 3JC,Hb2 small 3JN,Hb3
large 3JN,Hb2 small
16
HNHB, HN(CO)HB together

• can thus get both c1 angle and stereospecific
  assignments for bs from a combination of HNHB
  and HN(CO)HB

HNHB
HN(CO)HB
from Bax et al. Meth. Enzym. 239, 79.
17
Dihedral angle restraints

• derived from measured J couplings
• as with nOes, 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.
• 3JHa,HN(f)lt 6 Hz f -65 25
• 3JHa,HN(f)gt 8 Hz f -120 40