Transcript nOe distance restraints

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 tm’s used in an NOESY will be 20-200 ms.
from
Glasel &
Deutscher
p. 354
mixing time
basic NOESY pulse sequence
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 crossrelaxation.
nOe buildup will be faster for
larger proteins, which have a
longer correlation time tc, and
therefore more efficient zeroquantum 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
6
•these effects can be
avoided either by
sticking with short
mixing times or by
examining buildup
curves over a range of
mixing times
direct cross-relaxation
5
relative crosspeak intensity
•spin diffusion peaks
are usually observed
at long mixing time,
and their intensity
does not reflect the
initial rate of buildup
4
3
2
spin diffusion
1
0
note the delay in buildup
-1
0
50
100
150
mixing time
200
250
300
Other nOe caveats
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•
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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
strong
medium
weak
1.8-2.7 Å
1.8-3.3 Å
1.8-5.0 Å
strong intensity in short tm (~50 ms*) NOESY
weak intensity in short tm (~50 ms*) NOESY
only visible in longer mixing time NOESY
•
*for protein w/Mr<20 kDa
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.
• this calibration can then be used
to set intensity cutoffs for restraint
classes, often using a 1/r6 dependence
• ideally, one chooses
an internal standard
where the maximal nOe
will be observed (i.e.
something not undergoing a
lot of motion)
tyrosine
d-e distance
always the same!
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
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
Empirical Karplus relations in proteins
•
here are some empirical Karplus relations:
6.4 cos2(f - 60°) -1.4 cos(f - 60°) + 1.9
3J
2
Ha,Hb2(c1)= 9.5 cos (c1 - 120°) -1.6 cos(c1 - 120°) + 1.8
3J
2(c ) -1.6 cos(c ) + 1.8
(
c
)=
9.5
cos
Ha,Hb3 1
1
1
3J
2
N,Hb3(c1)= -4.5 cos (c1 + 120°) +1.2 cos(c1 + 120°) + 0.1
3J
2
N,Hb2(c1)= 4.5 cos (c1 - 120°) +1.2 cos(c1 - 120°) + 0.1
3J
•
Ha,HN(f)=
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)
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).
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
can’t tell the difference unless b’s are stereospecifically assigned
3D HN(CO)HB experiment
•
•
complementary to HNHB
measures 3JC,Hb couplings
for a particular b proton,
if q=180, 3JC,Hb= ~8 Hz
if q=+60 or -60, 3JC,Hb= ~1 Hz
Grzesiek et al. J. Magn. Reson. 95,
636 (1991).
HNHB and HN(CO)HB together
3J
C,Hb3=
small
3J
C,Hb2= large
3J
N,Hb3= small
3J
N,Hb2= small
3J
C,Hb3=
large
3J
C,Hb2= small
3J
N,Hb3= small
3J
N,Hb2= large
3J
C,Hb3=
small
3J
C,Hb2= small
3J
N,Hb3= large
3J
N,Hb2= small
HNHB, HN(CO)HB together
•can thus get both c1
angle and stereospecific
assignments for b’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.
6 Hz f= -65° ± 25°
3J
Ha,HN(f)> 8 Hz f= -120 ± 40°
3J
Ha,HN(f)<