Transcript What do we need to get a high

Recent advances in NMR structure
determination
• chemical shift potentials
• residual dipolar couplings
• Large proteins--TROSY and deuteration
Chemical shift potentials
• structure calculation suites such as X-PLOR and
CNS now incorporate the ability to directly refine the
structure against chemical shift, based on the ability
to accurately calculate chemical shifts from structure.
• the most commonly used potentials are for 13Ca and
13Cb chemical shifts and 1H chemical shifts
see Clore and Gronenborn, PNAS (1998) 95, 5891.
13C
chemical shift potentials
•
13Ca
and 13Cb chemical shifts are determined largely by the backbone
angles f and y, so potential energy functions can be used which
compare the observed chemical shifts to calculated shifts based on (f,
y) values in the structure being refined:
•
VCshift(f, y) = KCshift [(DCa (f, y))2 + (DCb (f, y))2]
•
where DCn (f, y)2 = Cnexpected (f, y) - Cnobserved (f, y), n=a or b, and KCshift
is a force constant arbitrarily chosen to reflect accuracy of calculated
shifts
1H
•
•
•
1H
chemical shift potentials
chemical shifts are a little more complicated to calculate from
structure--they depend on more factors
however, it has been shown that, given a high resolution crystal
structure, the 1H chemical shifts in solution can be predicted to within
0.2-0.25 ppm using a four term function: scalc = srandom + sring + sE + sani.
srandom is a “random coil value”, sring depends upon proximity and
orientation of nearby aromatic rings, sani is the magnetic anisotropy
resulting from backbone and side chain C=O and C-N bonds, and sE is
effects due to nearby charged groups.
1H
•
chemical shift potentials
so a 1H chemical shift potential would have the form
Vprot = Kprot (scalc, i - sobs,i)2
summed over all protons in the protein, where Kprot is a force constant and scalc,
i and sobs,i are calculated and observed shifts for proton i, respectively.
a portion of thioredoxin before
(blue) and after (red) 1H
chemical shift refinement--some
significant differences in the
vicinity of W31, which has an
aromatic ring that affects nearby
chemical shifts
Long-range information in NMR
•
•
a traditional weakness of NMR is that all the structural restraints are
short-range in nature (meaning short-range in terms of distance, not in
terms of the sequence), i.e. nOe restraints are only between atoms <5
Å apart, dihedral angle restraints only restrict groups of atoms
separated by three bonds or fewer
over large distances, uncertainties in short-range restraints will add up-this means that NMR structures of large, elongated systems (such as
B-form DNA, for instance) will be poor overall even though individual
regions of the structure will be well-defined.
long-range
structure bad
best fit
superposition
done for this end
short-range
structure OK
to illustrate this point, in the
picture at left, simulated
nOe restraints were generated
from the red DNA structure and
then used to calculate the
ensemble of black structures
Zhou et al. Biopolymers (1999-2000) 52, 168.
Residual dipolar couplings
•recall that the spin dipolar coupling depends on the distance between 2
spins, and also on their orientation with respect to the static magnetic
field B0.
•In solution, the orientational term averages to zero as the molecule
tumbles, so that splittings in resonance lines are not observed--i.e. we
can’t measure dipolar couplings. This is too bad, in a way, because this
orientational term carries structural info, as we’ll see
•In solids, on the other hand, the couplings don’t average to zero, but
they are huge, on the order of the width of a whole protein spectrum.
This is too big to be of practical use in high-resolution protein work
•compromise: it turns out that you can use various kinds of media, from
liquid crystals to phage, to partially orient samples, so that the dipolar
coupling no longer averages to zero but has some small residual value
Residual dipolar couplings: A Goldilocks tale
B0
B0
Proteins in a single crystal
Complete orientational bias
Enormous dipolar coupling.
Too big!
Proteins tumbling isotropically in solution
No orientational bias
Dipolar interaction averages to zero with
tumbling
No observable dipolar coupling.
(Dipolar couplings as big as
entire proton spectral range)
Too small!
...but the third bowl of porridge was just right.
B0
filamentous phage,
lipid bilayer fragment,
cellulose crystallite
Proteins dissolved in liquid but oriented medium
Some liquid crystals acquire macroscopic order in a magnetic field
e.g. bicelles, filamentous phage, cellulose crystallites
Collisions w/protein impart a slight orientational bias
A small “residual dipolar coupling” results
Just right! --> gives interpretable information
Measurement of Residual Dipolar Couplings
--regular HSQC
--decoupled in both
dimensions
--15N-1H splittings not
observed
--HSQC without
decoupling in 15N
dimension
-- isotropic solution
--15N-1H splittings
observed, equal to 15N-1H
one-bond scalar coupling
(~92-95 Hz)
--HSQC without
decoupling in 15N
dimension
--partly oriented
--15N-1H splittings
observed, equal to 15N-1H
one-bond scalar coupling
plus RDC!
Some RDC -, some +
Prestegard et al. Biochemistry (2001) 40, 8677.
This picture illustrates measurement of 15N-1H residual dipolar couplings
for a protein in a 7% bicelle (fragments of lipid bilayer) solution. The
bicelle preparation is isotropic (not ordered) at 25 °C (left), allowing
measurement of the scalar couplings. Upon heating to 35 °C, the bicelle
preparation becomes anisotropic (ordered) such that the measured
coupling now includes an RDC component. RDCs can therefore be
measured by comparing spectra taken at the different temperatures.
RDCs can often be “tuned” by adjusting the composition of the liquid
crystal mixture.
SAG: Strain induced alignment in a gel
pores in gel
contain
protein
regular polyacrylamide
gel
axially compressed,
radially stretched
oblate ellipsoid pores
radially compressed,
axially stretched
prolate ellipsoid pores
Proteins can be incorporated into cylindrical polyacrylamide gels within NMR
tubes. If the gel is stretched or compressed, the pores become anisotropic and
can impart partial order to a protein just like a liquid crystal can.
Interpretation of RDCs--what do they mean?
•
Recall that the spin dipolar interaction between two nuclei depends upon their
relative position with respect to an external magnetic field. The residual dipolar
coupling will therefore be related to the angle between the internuclear axis and
the direction of the partial ordering of the protein. See Tjandra et al. Nat Struct
Biol, 4, 732 (1997) for a more thorough treatment. Because the internuclear
axis will have a different orientation for different bonds in the protein, the RDCs
will exhibit a broad range of values.
internuclear axis (bond vector)
“axis of partial
ordering”:
principal axis
system of
magnetic
susceptibility
tensor
15N-1H
residual dipolar coupling will differ for
these two residues.
RDCs give information about long-range order in proteins
Note that the relative values of 15N-1H RDCs for a set of amide nitrogen
hydrogen pairs do not depend upon the distance between those pairs, only
on their relative orientation with respect to a common axis system!
15N
15N
1H
1H
two NH bond vectors
close together
15N
15N
1H
1H
two NH bond vectors far apart, but
with same orientation
In other words, RDCs can in principle tell us the relative orientation of two
bond vectors even if they are on opposite ends of the molecule. Contrast this
with NOE distance restraints and dihedral angle restraints which define short
range order.
Most measured RDCs are one-bond couplings
Recall that the spin dipolar interaction, and therefore the RDC, has both a
steep distance dependence and an orientational dependence. If we are
considering a particular type of RDC, say a one-bond coupling between
amide hydrogens and amide nitrogens, the interatomic distances are all the
same and equal to an NH bond length. The RDC depends only on the
orientational component. This would also still be true for a two-bond RDC,
but for a three-bond RDC the distance would vary with the dihedral angle,
making interpretation less straightforward.
Most measured RDCs are “one-bond”, e.g. between an amide proton and
its directly attached nitrogen, since these correspond to distances less than
< 1.5 Å generally. However, you’ll notice in the Chou paper that they
measure five dipolar couplings per residue, including HN, HC, CC and CN
one-bond couplings, but also including the 1Ha-13C’ two-bond coupling (C’
means the carbonyl carbon). So two-bond RDCs are not unheard of.
Illustration of effect of
using residual dipolar
couplings on the quality
of nucleic acid structure
determination by NMR
a) without rdc
b) with rdc
Zhou et al. Biopolymers (1999-2000) 52, 168.
Refining initial models with RDCs
A problem with dipolar couplings is that one cannot distinguish the direction of an
internuclear vector from its inverse. Thus the two opposite orientations below give
the same RDC value:
15N--1H
1H--15N
This ambiguity makes calculating a structure de novo (i.e. from a random
starting model) using only residual dipolar couplings very computationally
difficult. If there is a reasonable starting model, however, this is not a
problem. Thus residual dipolar couplings are especially good for refining
models/low resolution structures.
Large proteins--TROSY and deuteration
A major problem in NMR of large proteins is rapid transverse
relaxation (short T2), which leads to, among other things, very
broad lines. There are two major advances which address this.
TROSY
a method whereby line broadening effects due to rapid
transverse relaxation can be reduced or almost eliminated in
HSQCs by using cancellation of two major relaxation mechanisms,
the spin-dipolar interaction (which we talked about), and the
chemical shift anisotropy (which we did not). Price is some loss in
sensitivity.
Deuteration
Fractional or complete 2H labelling of proteins reduces the
magnitude of 1H-1H spin dipolar interaction, which as we have seen
is a major cause of rapid transverse relaxation for large proteins.
Can go as far as complete deuteration of nonexchangeable protons,
but of course then you won’t see the signal due to these protons.