Solving NMR structures Part I:
Experimentally derived restraints
1. Distance restraints
from crosspeak intensities in NOESY spectra;
measuring and calibrating NOEs
2. Dihedral angle restraints
from three-bond J couplings; measuring J couplings;
chemical shifts and dihedral angles
3. Hydrogen bond restraints
from amide hydrogen exchange protection data
4. Orientational restraints from residual dipolar
couplings (covered in a separate lecture)
1. 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
•
•
•
•
•
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 intensities
• 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!
2. Coupling constants and dihedral
angles
There exist relationships between three-bond scalar coupling constants
3J and the corresponding dihedral angles q, called Karplus relations.
These have the general form
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 that give a good fit between the coupling constants and the angles
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:
2(f - 60°) -1.4 cos(f - 60°) + 1.9
(
f
)=
6.4
cos
Ha,HN
3J
2(c - 120°) -1.6 cos(c - 120°) + 1.8
(
c
)=
9.5
cos
Ha,Hb2 1
1
1
3J
2(c ) -1.6 cos(c ) + 1.8
(
c
)=
9.5
cos
Ha,Hb3 1
1
1
3J
2(c + 120°) +1.2 cos(c + 120°) + 0.1
(
c
)=
-4.5
cos
N,Hb3 1
1
1
3J
2
N,Hb2(c1)= 4.5 cos (c1 - 120°) +1.2 cos(c1 - 120°) + 0.1
3J
•
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 spectra
ratio of crosspeak
and diagonal peak 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 experiment
• similar to HNHA but measures 3JN-Hb couplings
instead
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)
This accounts for errors in measurement as well as the
fact that the Karplus relation itself is not exact.
Chemical shifts and backbone
conformation
•
•
•
•
chemical shifts depend upon local electron distributions, bond
hybridization states, proximity to polar groups, nearby aromatic rings,
local magnetic anisotropies.
in other words, chemical shifts depend upon the structural environment
and thus can provide information about structure
observation of relationships between chemical shifts and protein
secondary structure has led to the development of some useful
empirical rules
The most common of these rules relate to backbone conformations
(combinations of dihedral angles)
Ha chemical shifts and
secondary structure
•
•
•
Ha chemical shifts are generally lower
for a-helices than for b-sheets
the figure at right shows distributions
of Ha chemical shifts observed in
sheets (lighter bars) and helices
(darker bars). The black bar in each
distribution is the median.
Ha chemical shifts in a-helices are on
average 0.39 ppm below “random coil”
values, while b-sheet values are 0.37
ppm above random coil values.
Wishart, Sykes & Richards
J Mol Biol (1991) 222, 311
.
Chemical shift index (CSI)
•
•
•
trends like these led to the development of the concept of the chemical
shift index* as a tool for assigning secondary structure using chemical
shift values.
one starts with a table of reference values for each amino-acid type,
which is essentially a table of “random coil” Ha values
CSI’s are then assigned as follows:
exp’tl Ha shift rel. to reference
within ± 0.1 ppm
>0.1 ppm lower
>0.1 ppm higher
assigned CSI
0
-1
+1
*Wishart, Sykes & Richards Biochemistry (1992) 31, 1647-51.
Chemical shift indices
CSI
residue #
•
•
•
•
•
•
one can then plot CSI vs. sequence and assign 2ndary str. as follows:
any “dense” grouping of four or more “-1’s”, uninterrupted by “1’s” is assigned as
a helix, while any “dense” grouping of three or more “1’s”, uninterrupted by “-1’s”,
is assigned as a sheet.
a “dense” grouping means at least 70% nonzero CSI’s.
other regions are assigned as “coil”
this simple technique assigns 2ndary structure w/90-95% accuracy
similar useful relationships exist for 13Ca, 13Cb 13CC=O shifts
Here’s a figure showing deviations of Ca and Cb chemical shifts
from random coil values when in either a-helix or b-sheet conformation
for a-helices, Ca shifts are higher than normal, whereas
Cb shifts are lower than normal.
Chemical shifts and structural restraints
•
•
•
•
•
CSI is a very widely used technique for quickly and qualitatively assigning
secondary structures from chemical shift data.
Restraints on structure for use in explicit structure calculations are also derivable
from chemical shifts, analogous to our nOe-derived distance restraints, our
coupling-constant-derived dihedral angle restraints and our hydrogen-exchange
derived hydrogen bond restraints.
These restraints often take the form of potential functions. For example, 13Ca
and 13Cb chemical shifts are determined largely by the backbone angles f and y,
so potential functions can be used to restrain these angles to values near to
those expected based on the observed shifts.
Such potentials can supplement the use of J-couplings in restraining dihedral
angles.
Such potentials are not in very wide use in structure calculations yet and we will
not cover them further here. The interested student should see Clore and
Gronenborn PNAS (1998) 95, 5891 for a review of this topic.
3. Amide hydrogen exchange and H-bonds
•amide protons undergo acid- and base-catalyzed exchange with
solvent protons at a rate which ranges from the second to minute time
scale, depending upon solvent conditions (mostly pH)
•if a protein is placed in D2O, the amide signals due to 1H nuclei will
disappear over time due to this exchange
half-life
exchange rate
poly-D,L-alanine
exchange rate in D2O
at 20 °C. Minimum with
respect to pH is due to
the fact that exchange is
both acid and base
catalyzed
Englander & Mayne, Ann. Rev. Biophys. Biomol. Struct. (1992) 21, 243.
pH but in D2O!
Amide hydrogen exchange
•
when amide protons are involved in hydrogen bonds in a folded protein,
they are protected from exchange with solvent and thus exchange
somewhat more slowly, i.e.
faster:
N-H --> N-D
slower:
N-H....O=C --> N-D....O=C
Protection factors
•
the protection factor P for a given amide proton is the intrinsic rate of
exchange expected for that amide proton in an unfolded protein under
a given set of solvent conditions, divided by the observed rate of
exchange in the native state
P= kex(U)/kex(N)
where U is the unfolded state and N is the native state
•
intrinsic rates of exchange vary with the amino acid sequence and the
solvent conditions in a predictable manner--there are published tables
and websites where you can look them up/calculate them.
Measuring amide exchange rates
•
•
15N-1H
HSQC spectra are a good way to monitor exchange because
individual well-resolved peaks are visible for most amides
one might record a spectrum in H2O, freeze dry the sample, resuspend
in D2O, and record a series of spectra in D2O to monitor the rate at
which each amide proton disappears
picture at left:
15N-1H HSQC of Arc repressor 5 min
after resuspension in D2O (pH 4.7)-note that unprotected amides such as
the unstructured N-terminus (1-7) have
already exchanged. This is because
intrinsic half-lives at this pH are in the
vicinity of 10 seconds to a minute.
Burgering et al. Biopolymers (1995) 35, 217.
The plot above shows measured exchange rates from a series of 15N-1H
HSQC spectra for Arc repressor. Protected amides are usually within
secondary structure elements, but the presence of secondary structure
doesn’t guarantee that protection will be observed (note the lack of
protection for the beta-sheet from residue 9-14). Lack of protection could
indicate that the secondary structure element undergoes fairly rapid local
unfolding. Note the strength of NMR and HSQC in particular here--you get
a separate exchange rate for every amide proton--great residue-specific
dynamic information!
HX (hydrogen exchange) of Syrian hamster
prion protein
surface is less well-protected
ends of helices less well-protected
blue spheres: P > 4650
green spheres: 370 < P < 4650
red spheres: P < 370
note that while all protected
amides are hydrogen-bonded,
not all hydrogen-bonded
amides are equally well
protected. Rates differ both
within secondary structure
elements (buried positions
near the center usually most
protected) and between
different secondary structure
elements
Liu et al. Biochemistry (1999)
38, 5362.
Hydrogen bond restraints
•
•
•
amide protons showing significant protection are inferred to be involved
in hydrogen bonds, but it is not clear from this data alone what the
identity of the hydrogen bond acceptor group is.
however, if additional information is available, one can infer what the
acceptor is. For instance, daN(i-3,i) and daN(i-4,i) nOe’s such as are
characteristic of a-helices imply that the protected amide of residue i is
hydrogen bonded to the carbonyl of residue i-4.
hydrogen bond restraints are usually expressed as a pair of distance
restraints, e.g dHN-O = 1.5-2.3 Å, dN-O = 2.5-3.3 Å. A pair of restraints
like this ensures reasonable good geometry for the hydrogen bond.