THE RIGAKU JOURNAL
VOL. 9 / NO.2
/ 1992
Contributed Papers
DIFFUSE SCATTERING FROM CRYSTALS OF YEAST INITIATOR
tRNA
ANAND
R. KOLATKAR, JAMiS
B. CLARAGE, AND GEORGE N. PHILLIPS, JR.
Rice University, Dept. of Biochemistry and Cell Biology,
PO Box 1892, Houston, TX. 77251
1.
Introduction
X-ray crystal structure analysis can provide a
good deal of detail about the average structure of
a macromolecule.
During the refinement process,
regions of the molecule are sometimes found to
be disordered;
high B-factors and poorly defined
electron density indicate the absence of a single
well-ordered
conformation.
While data reduction
programs are quite adept at extracting the usable
Bragg intensities from the diffraction image, information in the form of diffuse X-ray scattering is
excluded from the structural
analysis scheme for
proteins and nucleic acids. This unused scattering
contains information
about disorder between and
within molecules in the crystal. Unlike B-factors,
however, diffuse scattering can distinguish between
uncorrelated and correlated motions.
Analysis of diffuse scattering from tropomyosin
crystals reveals considerable motion in the filamentous protein lattice [1,2]. Similarly, insulin crystals
have been shown to contain movements that are
predominantly
correlated over distances of approximately 6 A [3]. Short-range coupled motions have
also been found to dominate in triclinic and tetragonal lysozyme crystals [4]. Orthorhombic
lysozyme
crystals produce diffuse streaks which have been
simulated by a long-range lattice-coupled model [5].
Diffuse scattering from crystals of a DNA octamer
revealed partially disordered B-DNA present in the
solvent channels formed by A-DNA [6]. In this
paper we describe the analysis of X-ray diffuse
scattering exhibited by yeast initiator tRNA crystals.
The structure of yeast initiator tRNA (space group
P6422) has been solved to 3 A resolution [7,8]. The
acceptor arms of adjacent tRNA molecules line up
to form a pseudo-helix along the c axis of the unit
cell with the anticodon arms extending out almost
perpendicularly
from this pseudo-helix
axis (see
4
Fig. I). Adjacent pseudo-helices contact each other
through their extended anticodon loops. The electron
density for the anti-codon loop region, however, is
not localized, and B-factors are quite large in this
part of the tRNA molecule. Solvent content in this
crystal form is high (approximately
85%) indicating
that there is room for large scale molecular motions
in the unit cell.
2.
Diffuse Scattering Features
Initial characterization
of the diffuse scattering
from yeast initiator tRNA has briefly been described
previously [9,10]. The data used in this analysis has
been collected on imaging plates using synchrotron
radiation at the Photon Factory (Japan) using Fuji
Imaging Plates [8]. The diffraction
from these
crystals reveals various forms of diffuse scattering
(Fig. 2). The most striking of these features are the
streaks seen in the lower left and upper right corners
of the diffraction image.
The location of the streaks of diffuse scattering
can be compared with the corresponding
crystal
orientation.
Figure 2 shows an image of tRNA
X-ray scattering which corresponds to the unit cell
orientation shown in Figure 1. In the imaging plate
image, the c* axis runs from the lower left corner
to the upper right corner. Similarly, in the unit cell
drawing, the c axis runs in the same direction. The
diffuse streaks run perpendicular to the c* axis and
also to the pseudo-helix lying along the c axis. If
some coherently moving unit were moving parallel to
the c axis, diffuse scattering oriented perpendicular
to and situated along the c* axis would be expected.
To test this hypothesis, the diffuse scattering from
such a model is calculated and compared to the
actual imaging plate data. The correctness of the
model is determined by the degree of similarity between the calculated and observed diffuse scattering.
The Rigaku Journal
a
.:
c
Fig. 1 Line drawing of yeast initiator tRNA molecules. Note that the acceptor arms lie along the c axis
while the anti-codon loops extend in directions perpendicular to the c axis. This view corresponds to the
orientation of the diffraction image in Fig. 2.
Another diffuse feature seen in the imaging plate
image is the very diffuse cloud of scattering. The
location of the cloud, the bulk of which lies perpendicular to the c axis at large values of a*, together
with the fact that the disordered anti-codon loops
lie perpendicular
to the c axis imply that the very
diffuse scattering is the result of some type of motion
in the anti-codon region. Since this diffuse feature is
not associated with Bragg positions, the disorder
producing this scattering is due to some type of
short-range coupled motion.
Computational Procedure
The rationale
behind these simulations
is to
reproduce the diffuse scattering features seen on the
imaging plate image. Once the simulation is made to
match the observed diffraction, the parameters used
in the simulation provide specific information about
the nature of the disorder producing the diffuse
features. Two different computational
methods were
used to calculate the various diffuse scattering
components. The streaks and halos were modelled
using a convolution-based
technique. Motions which
are not highly coupled were simulated as independent
motion components.
The streaks and halos are localized to Bragg
positions. These features were simulated by convoluting the Bragg peaks with an appropriate
halo
function which describes the correlation among the
tRNA molecules [4]. The actual convolution proce-
dure is given by F;(R)*f
where f = [FT[r(r)]],
r is
the radial coordinate in Patterson space, and the *
symbol denotes the convolution operation. F;(R) is
the ideal structure factor calculated from the atomic
coordinates for yeast initiator tRNA assuming no
atomic motion. The form of this halo function
determines the shape of the diffuse feature at a
Bragg position. A spherically symmetric function, i.e.
r(r)=e-r/y,
produces a spherical halo. It is clear
from the imaging plate data that the streaks are not
spherically symmetrical about the Bragg positions so
that r(r) takes the form
3.
Vol. 9
No.2
1992
(1)
to account for the anisotropy. The values of Yx, YY'
and Yz can be adjusted separately to achieve the
appropriate anisotropic function.
The diffuse features produced by intramolecular
disorder were simulated using electron density models
in which disorder was included. The total scattered
intensity is given by
IT(R)
= <I FTp(rW)
(2)
The diffuse scattering intensity was calculated
cording to the following equation
ID(R)
= <I FT per) 12) -I FT < per)~ 12
ac(3)
which is simply the difference between the total and
Bragg scattering where the symbol
denotes the
< )
5
Long-range
acceptor stem
correlated motion
Antl-codon stem
correlated motion
Antl-codon stem
Independent motion
Independent atom
motion
Water diffraction
Fig. 2 Simulation
of the scattering from yeast initiator tRNA. The experimental
image (top left)
corresponds to a IS rotation photograph
recorded using 1.3 A radiation on imaging plates set 200 mm
from the crystal. The experimental
diffraction and the diffuse scattering simulation
(top right) are
colored such that the least intense features appear blue. Intermediate
intensities are pink and the most
intense features appear white. The five components
comprising the diffuse features of the scattering
simulation are shown individually along the bottom.
Fig. 3 Magnification of the experimental (left) and simulated (right) diffraction images. The upper right
hand quadrant of each of these images shows a close correspondence
in the diffuse streaks and halos.
6
The Rigaku Journal
average over all unit cells. Specifically, the electron
density, per), was built assuming a three Gaussian
approximation
of the atomic scattering factor for
each atom [11,12]. Each unit cell contains the
electron density of twelve tRNA molecules where the
atoms in each molecule have been displaced from
their average position according to some model of
motion. The total scattering, <I FTper) 12), is calculated by Fourier-transforming
each unit cell, squaring the result, and then averaging over all unit
cells in the simulation. Similarly, the Bragg scattering, 1 FT<p(r)
12, is calculated by first averaging the
electron density over all unit cells and then Fouriertransforming and squaring the average.
The very diffuse cloud of scattering was modelled
using the direct technique described above. One
component contains the calculated diffraction from a
model in which each atom in tRNA moves randomly
and also independently
of every other atom. The
other component
contains the diffraction from a
model in which the anti-codon loop region moves
independently and as a coherent unit. Depending on
the model, the amplitude of motion is determined by
the root-mean-square
displacement calculated from
either the crystallographic
B-factor for each atom or
from the mean B-factor for the anti-codon
loop
region. In the case of each atom of tRNA moving
independently, the rms displacement of 0.89 A used
in the simulation compares well with the rms displacement value of 0.86 A calculated from the mean
B-factor (59.7 A 2) for all atoms. A rms displacement
of 1.1 A calculated from the mean B-factor (102.6 A 2)
for bases 22-46, was used in the calculation of diffuse
scattering from the anti-codon loop region moving as
a coherent unit. Two hundred unit cells containing
electron density calculated according to one of the
models described above are created and then Fouriertransformed
yielding the calculated diffraction. A
final step in all simulations involves the projection .'
of the simulated intensities intersecting the Ewald
sphere (oriented to match the diffraction
image
orientation) onto the film plane.
4.
Results and Discussion
The calculated diffuse scattering provides information regarding the direction of motion as well as the
size of the coherently moving unit. The total scattering simulation (Fig. 2) includes six components
• Bragg intensity
• Long-range acceptor stem correlated motion
• Anti-codon stem correlated motion
• Anti-codon stem independent motion
• Independent atom motion
• Bulk water diffraction
All these components, except Bragg diffraction, are
also displayed separately in Fig. 2. Bulk water
Vol.9
No.2
1992
diffraction is included in the simulation to account
for the circularly symmetrical
scattering. Experimental X-ray intensity curves for bulk water were
used to produce the water diffraction component
seen in Fig. 2 [13]. The tRNA crystals contain
approximately
85% water contributing significantly
to the spherically symmetric scattering. Inclusion of
this component provides a better fit to the observed
diffraction especially at higher resolutions (3-4 A).
Streaks and halos at Bragg positions indicate that
correlated motions contribute to the total scattering
observed on the imaging plates. Simulation of the
streaks indicates that the coherently moving unit has
a size of approximately
one unit cell distance along
the c axis (136.5 A). Note that the acceptor stems,
which are 60 A in length, of each tRNA molecule lie
almost along the c axis forming a pseudo-helix. This
immediately suggests that the coherent unit consists
of two adjacent tRNA molecules lying along the c
axis. Correlation along the other two axes is much
less coupled (30 A). Adjacent pseudo-helices contact
each other via their anti-codon loop regions allowing
pseudo-helices to be coupled to nearest neighbors
with a coupling distance of 113 A along the other
two unit cell directions. Standard crystallographic
analysis, however, shows the terminal half of the
anti-codon
loop region to be highly disordered,
thereby limiting coupling between adjacent pseudohelices. Furthermore,
the more well-ordered half of
the anti-codon
loop would account for the 30 A
coupling distance along the a and b directions.
The diffraction from an all atom independent
motion calculation produces spherically symmetric
diffraction. While this scattering may appear, on first
glance, to be similar to diffraction by water, there is
a key difference. Namely, as a function of resolution,
diffraction from bulk water peaks at around 3.3 A
while diffraction
from an all atom independent
motion model (protein or nucleic acid) generally
peaks at lower resolution depending on the amplitude
of motion of the protein atoms. Thus, each of these
components contributes diffracted intensity at different resolutions.
Independent motion for a larger coherent unit, the
anti-codon loop region, produces spherically asymmetric diffraction. In this calculation, all atoms of the
terminal region of the anti-codon stem are subject to
the same displacement (based on the mean B-factor
for this region). The anti-codon
regions of each
molecule are displaced independently
of all other'
molecules. The size of the coherently moving unit is
somewhere between an individual atom and a whole
molecule producing diffraction which is somewhere
between spherically symmetric and Bragg-associated
diffraction. By changing the coherent unit size, then,
it is possible to model a range of diffraction features.
7
The successful simulation of the diffuse scattering
provides information which is complementary to that
provided by standard X-ray crystallography.
While
crystallography
provides a static average structure,
analysis of the diffuse scattering reveals the dynamic
nature of the molecules. Both long-range coupled
motions of whole molecules and short-range coupled
motions within a molecule contribute to the overall
disorder in yeast initiator tRNA crystals. A model
which includes deviations from the average structure
more accurately depicts the states of molecules in a
crystal.
Acknowledgements
We would like to thank Prof. P. Sigler and Dr. R.
Basavappa for the yeast initiator tRNA diffraction
data and structural coordinates. We also thank the
Molecular Structure Corporation
for commitments
to help provide imaging plate technology for diffuse
scattering studies and Polygen for Quanta software.
This work supported by grants Welch C-1142 (GNP),
NSF DMB 87-16507 (GNP), NIH Training Grant
(ARK), NIH NRSA Postdoctoral
Fellowship GM13945 (JBC), and the W. M. Keck Center for
B
Computational
Biology.
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