Recent advances in NMR structure determination

1
Recent advances in NMR structure determination

• chemical shift potentials
• residual dipolar couplings
• Large proteins--TROSY and deuteration

2
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.
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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), na or b, and KCshift is a
  force constant arbitrarily chosen to reflect
  accuracy of calculated shifts

4
1H chemical shift potentials

• 1H 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 CO and C-N bonds,
  and sE is effects due to nearby charged groups.

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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
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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 lt5 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
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
best fit superposition done for this end
short-range structure OK
Zhou et al. Biopolymers (1999-2000) 52, 168.
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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
  cant measure dipolar couplings. This is too
  bad, in a way, because this orientational term
  carries structural info, as well see
• In solids, on the other hand, the couplings dont
  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

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Residual dipolar couplings A Goldilocks tale
B0
B0
Proteins tumbling isotropically in solution No
orientational bias Dipolar interaction averages
to zero with tumbling No observable dipolar
coupling. Too small!
Proteins in a single crystal Complete
orientational bias Enormous dipolar coupling. Too
big! (Dipolar couplings as big as entire proton
spectral range)
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...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 Collisio
ns w/protein impart a slight orientational bias
A small residual dipolar coupling results Just
right! --gt gives interpretable information
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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
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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.
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SAG Strain induced alignment in a gel
pores in gel contain protein
axially compressed, radially stretched oblate
ellipsoid pores
radially compressed, axially stretched prolate
ellipsoid pores
regular polyacrylamide gel
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.
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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.
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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
1H
15N
1H
15N
15N
1H
1H
two NH bond vectors far apart, but with same
orientation
two NH bond vectors close together
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.
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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 lt 1.5 Å
generally. However, youll 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.
16
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.
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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.
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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 wont see the signal due to
these protons.