Incorporating additional types of information in structure calculation: recent advances

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Incorporating additional types of information in
structure calculationrecent advances

• chemical shift potentials
• residual dipolar couplings

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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

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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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• the residual dipolar coupling will be related to
  the angle between the internuclear axis and the
  direction of the partial ordering. The equations
  for this are given in Tjandra et al. Nat Struct
  Biol, 4, 732 (1997), which I will hand out as
  supplementary reading on Monday. Now suppose we
  have two different residues in a protein and we
  are measuring the residual dipolar coupling
  between the amide nitrogen and amide hydrogen

internuclear axis
axis of partial ordering principal
axis system of magnetic susceptibility tensor
15N-1H residual dipolar coupling will differ for
these two residues. This difference depends on
the relative orientation of the two NH groups,
but not on the distance between them
long-range information!
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Prestegard et al. Biochemistry (2001) 40, 8677.
this picture shows 15N-1H residual dipolar
couplings measured in an 15N-1H HSQC spectrum of
a protein sample partially oriented using
bicelles (fragments of lipid bilayer). One of
the nice things about residual dipolar couplings
is that they are easy to measure.
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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 orientations below give the same dipolar
coupling
1H--15N
15N--1H
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. So residual dipolar couplings are
especially good for refining models/low
resolution structures.