Transcript What do we need to get a high

Incorporating additional types of
information in structure calculation:
recent advances
• chemical shift potentials
• residual dipolar couplings
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
•
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
long-range
information!
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
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.
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 orientations below give the same dipolar
coupling:
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. So residual dipolar
couplings are especially good for refining models/low resolution
structures.