Crystallographic Methods and Protocols

388 Pages·1996·24.224 MB·English

by  Christopher Jones, Barbara Mulloy, Mark R. Sanderson

CHAPTER 1
Introduction
Mark R. Sanderson
This chapter is intended to give an overall view of the process of struc-
ture solution with some of the basic theory behind it. It is possible to skip
the most mathematical section, at any rate, on a first reading. There is a
bibliography at the end of this chapter that should provide further read-
ing matter for readers at every level of crystallographic experience.
1.1. Fundamentals of X-Ray Difiaction
X-rays are a form of electromagnetic radiation, with a shorter wave-
length than radio waves or visible light. X-rays are used in crystal studies
because their wavelength (1.542 x l&lo m for copper K cx radiation) is
comparable to the planar separation of atoms in a crystal lattice, if the
Bragg description of diffractron from a crystal is considered. The Ang-
strom unit, where 1 A = lo-lo m, is still widely used in diffraction circles.
Measurements in these units, rather!han their SI equivalents, can be spo-
ken in fewer syllables (e.g., 1.547 A, compared with 0. 1547 nm).
Safety: It must be stressed that X-ray equipment must under no
circumstances be used by an untrained operator. Training in its use
must be received from an experienced worker.
1.1.1. X-Ray Generation
X-rays are generated when a beam of electrons at a potential of approx
10,000 eV is accelerated from a small tungsten filament (the cathode) to
strike an anode (usually a copper target for macromolecular studies).
The deceleration of these electrons, which is known by its German name
bremsstrahlung, causese lectrons to be knocked out of the inner K and A4
From Methods in Molecular Bology, Vol 56 Crystallographx Methods and Protocols
Edlted by C Jones, 6 Mulloy, and M Sanderson Humana Press Inc , Totowa, NJ
1
2 Sanderson
0.5 1.0 1.5 2.0 2.5
Wavelength (A)
Fig. 1. X-ray spectrum of MoKa, 50 kV, and CuKa, 35 kV The absorption
spectrum of nickel is shown by the dotted lme.
atomic shells and dissipates a large amount of heat. When the electrons
in higher levels fall back to these inner shells, emission of X-ray radia-
tlon occurs. When the transitions are from K to L, then K al and K a2
radiations are produced, whereas the transition from M to K leads to K
p 1 and K p2 radiation. Since the electrons are involved m multiple colli-
sions, these defined lines are superimposed on a background of white
radiation. Figure 1 shows a typical X-ray emission spectrum. In macro-
molecular studies, copper K a radiation is usually used with the K p
filtered out either by a graphite monochromator or by nickel filters.
Molybdenum radiation of wavelength 0.71 f\ is often used m small
organic and inorganic molecule diffraction studies, but has also been used
for several high-resolution protein data collections.
An alternative source of X-rays is synchrotron radiation, which is gen-
erated tangentially to a ring of accelerating electrons. This source of
X-radiation is available at various centers throughout the world, such as
the Daresbury Laboratories (Warrington, UK), Brookhaven National
Laboratories ( Long Island, NY), The Photon Factory (Japan), L.U.R.E.
(Paris, France), and the E.S.R.F. (Grenoble, France). Synchrotron radia-
tion offers the possibility of tuning the X-ray wavelength to suit the prob-
Introduction 3
lem being studied, as discussed by Krishna Murthy in Chapter 5, and it
has a beam with narrow divergence, resulting in small spot sizes, which
is a great advantage when studying viral crystals as discussed by Eliza-
beth Fry et al. in Chapter 13. The X-ray flux attainable at synchrotron
rings is also much higher than that generated in a conventional X-ray
laboratory, often allowing higher-resolution data to be collected in a
shorter time. Research groups apply for “beam time” at these centers,
travel to the synchrotron with their crystals, and collect data during then
allocated period. Two types of generators are in general use in X-ray
diffraction laboratories, known as sealed-tube generators and rotating
anode generators.
1.1.1.1. SEALED-TUBE GENERATORS
These X-ray sources consist of a sealed evacuated glass tube contain-
ing a filament and a fixed hollow target anode, which is cooled by water.
Generators fitted with these tubes produce X-rays of up to 3 kW, corre-
sponding to a current of 50 mA and voltage of 60 kV. Heat generated by
the decelerating electrons means that these tubes cannot be operated at
very high powers since the anode will melt. The advantage of sealed-
tube generators is that they require less maintenance than the rotating
anode generators described below, and the sealed tube may easily be
replaced at the end of its lifetime. The major disadvantage of these sys-
tems is the limit on the operating power of a fixed target source, which
results in lower X-ray fluxes compared with those from rotating anode
generators.
1.1.1.2. ROTATING ANODE GENERATORS
Rotating anode generators were developed in order to increase the
X-ray flux. The filament is mounted in a focal cup in the electron gun,
and the electron beam is directed at a rotating anode (usually copper).
The anode is spun so that a cooler region of the copper anode is continu-
ally brought into the path of the X-ray beam. This allows higher powers
to be used without melting the target. Here again, the rotating copper
wheel is water-cooled, often on an internal circuit that is heat-exchanged
against an external cooling loop. Figure 2 shows a Rigaku RU-200 X-ray
generator, with the rotating anode mounted on top of the stainless-steel
column. In this generator, X-rays can exit from two ports (to the left and
to the right), sealed by an-tight beryllmm windows, which are transpar-
ent to X-rays. In the figure, only the right-hand port is in use and has an
Sanderson
Fig. 2. Rigaku RU-200 X-ray generatorw ith a mirror system and an R-AXIS
II image plate detector mounted against the right port (courtesy of Dr. Paul
Freemont, I.C.R.F.).
X-ray mirror system and image plate detector mounted against it (Rigaku
Raxis II, image plate detector; X-ray mirrors developed by Z. Otwinowsky
and marketed by Molecular Structure Corporation). The electron gun is
evacuated to 10M5P a by a turbomolecular pump, which is backed on to
an oil diffusion pump. These generators typically operate at a power of
5.4 kW when a small filament (300 pm) is used and 12 kW when a broad
focus (500 pm filament) is used. Recently, X-ray sources have become
available with more compact, high-voltage generators. The older instru-
ments have oil immersed high-voltage tanks, which take up much more
floor space, an important consideration when laboratory space is limiting.
1.2. Crystals and Symmetry
A crystal may be thought of as a three-dimensional lattice of mol-
ecules. An early study of crystal morphology of quartz in 1669 by a Dan-
ish physician, Nicolaus Steno, concluded that the angles between similar
crystal faces were the same. At the end of the 18th century, Abbk Hauy
Introduction 5
and Romk de 1’Isle extended these observations to other crystals, and
found that the interfacial angles were the same even though the overall
morphology of the crystals may be very different. Bravais showed that
symmetry criteria limited the number of lattices to the 14 lattices shown
in Fig. 2 of Chapter 3. It was known even before the discovery of X-rays,
through the mathematical studies of Federov in Russia, Schoenflies in
Germany, and Barlow m Britain at the turn of the century, that there 1s
only a finite number of ways of arranging objects symmetrically wlthin a
crystal lattice. This gives rise to the 230 possible space groups, which are
listed in International Tables for Crystallography, published by Rediel
NEKluwer Academic Publishers, Norwell, MA. A copy of these tables
should be available to anyone wishing to work in crystallography.
For biological studies, we need only consider 65 out of the 230 pos-
sible spaceg roups, becausem acromolecules are chiral and therefore only
those space groups lacking a center of symmetry need be considered.
The subject of crystal symmetry is discussed more fully in Chapter 3.
1.2.1. Miller Indices
The crystal may be thought of as sectioned into planes as shown below
(Fig. 3). Miller indices are the three intercepts that a plane makes with
the cell axes, in units of the cell edge. For example, if the plane intersects
the axes of a cell with lengths a, b, and c at coordinates a’, b’, and c’, then the
Miller indices are given by h = a/a’, k = b/b’ and I = c/c’.
1.2.2. Diffraction from Lattices
The crystal may be viewed, by analogy with the difiaction of visible light,
asa three-dimensionalg rating,w ith the diffracted rays interfering in phasea nd
out of phaset o produce a diffraction pattern.T he spacingo f the resulting pat-
tern is inversely proportional to the lattice spacing as given by Bragg’s law:
nh = 2dsm 8 (1)
where h = wavelength, 6 = diffraction angle, d = lattice spacing,a nd n = dif-
fraction order. Figure 4 shows the derivation of Bragg’s law. Two incident
rays are shown with a path difference given by A(path) = PQ + QR = nh.
1.2.3. Resolution
Having crystals that diffract X-rays to large values of 8 IS vital to being
able to solve a structure so that biological detail may be extracted. When
a crystallographer is found talking about a new crystal form diffracting
to the edge of the film (on a precession camera with a crystal-to-film
6 Sanderson
b
l l -
b’,
a’ a
A
C
b
t. a
C
010 110
@
iii
Fig. 3. Miller indices of lattice planes wlthin a crystal. (A) A Lattice plane
with intercepts a’, b’, and c’ along the a, b, and c axes. (B) Lattice planes m a
two-dimensional lattice. (C) Lattice planes m a three-dimenslonal lattice.
(Reproduced with perrmssion from ref. I.)
distance of 10 cm), this is often a cause for celebration, since the data
once collected and processed from this crystal form will allow the
polypeptide backbone to be traced (for a protein) or unambiguous posi-
tioning of the backbone and bases (for a nucleic acid). Equation 1 may be
rearranged as d = h/2 sin 8, since we are considering first-order diffrac-
tion with YI = 1. Substituting for the diffracting angle 0 gives the useful
form of the equation d = h/2 sin [( 1/2)tan-’ (r/F)] where r is the distance
of a diffraction intensity from the center of the film and F is the crystal-
Introduction 7
82 +8 3 =nh (4
I% = O’R = d srn 0 04
Substltutlng (b) Into (a) gwes
2dslnO=nh
Fig. 4. The derivation of Bragg’s law.
to-film distance (10 cm for many precession cameras). Further details of
preliminary crystal characterization are discussed in Chapter 3 by Sherm
Abdel-Meguid et al. Figure 5 shows the diffraction pattern from a crystal
of the thymidme kmase from herpes simplex vn-us type 1, which has
been mounted together with a small amount of buffer in an X-ray capil-
lary tube (Fig. 6) and irradiated with X-rays. Since water is an integral
part of the crystal lattice, crystals must be mounted and kept hydrated, a
very important observation first made by Hodgkin and Bernal (2). Flash-
freezing crystals to liquid nitrogen temperatures may also be used to
maintain the lattice hydration as described in Chapter 3. The reflections
recorded in this 2” oscillation photograph may be assigned indices h, k,
and 1 and their intensities I(hkl) measured by using integration software.
The photograph shows a distorted picture of the reciprocal lattice. In the
past, precession X-ray cameras were used to give an undistorted view of
the reciprocal lattice, which facilitated space group assignment, and
indexing of the reflections, when this was done by hand.
1.3. An Overview
of Macromolecular Crystal Structure Solution
This section shall give a brief nonmathematical overview of macro-
molecular structure solution, leaving a more detailed treatment for later
m the chapter (Section 1.4.).
8 Sanderson
Fig. 5. Diffraction of thymidine kinase from herpes simplex virus type 1
recorded on an MAR image plate detector. (M. R. Sandersona nd W. C. Sum-
mers, unpublished results.)
1.3.1. Stage 1: Protein Preparation and Crystal Growing
1. The first stagei n a crystallographic study is to obtain tens of milligrams of
the macromolecule (or macromoleculesw hen the structure of a complex is
being undertaken) in a very pure form, either from:
a. A natural source rich in the protein;
b. The use of cloning techniquest o engineera vector that will overexpress
the desired macromolecule in large amounts; or
c. Chemical methods, as in the case of DNA synthesis for DNA
crystallization.
Chapter 2 covers aspects of genetic engineering. Biochemical tech-
niques are used to purify the macromolecule; this can usually be achieved
in fewer steps with cloned material. An affinity “tag” is often attached in
order to aid purification, although cleaving the tag away from the molecule
Introduction
I 3g. 6. Crystal of thymidine kinase mounted in a glass capillary tube and
attac hed to a goniometer head using plasticine. The arcs and sledges on the
wn nometer head allow the crystal to be centered in the X-ray beam.
of interest may introduce heterogeneity, which hampers crystallization.
The knowledge of solubility in different buffer solutions at different salt
concentrationsg ained by biochemical manipulation of the protein can often
be very useful when crystallizations are set up.
10 Sander-son
2. Crystalhzatron of protems IS discussed in Chapter 2, of DNA and protem-
DNA complexes m Chapter 12, and for membrane protems m Chapter 14
1.3.2. Stage 2: Symmetry Determination
The symmetry of the macromolecular crystals is determined as dis-
cussed in Chapter 2. If the crystals are found to be sensitive to radiation
damage in initial experiments, then cooling techniques, also discussed m
Chapter 2, may be used to extend the crystal lifetime. Macromolecular
crystals are formed of molecules that are chiral, so only the 65 space
groups that lack a center of symmetry need be considered.
1.3.3. Stage 3: The Strategy for Structure Solution
1. The strategy for structure solutton wrll depend on whether or not a stmrlar
macromolecule, or fragment of it, has been solved before, and the coordr-
nates are avatlable.
2 If coordmates are obtainable, then the structure may be solved by molecular
replacement usmg the phase mformatton from the prevrously solved struc-
ture, and only a natrve X-ray diffraction data set needs to be collected. “Natrve
data” are crystallographlcjargon describing data collected from crystals m
then native state, unmodtfied by, for example, heavy-atom dertvatizatton
3 If a structurally related macromolecule has not been solved, then the phase
mformation has to be obtained “de ~OVO” from either several heavy atom
derrvatrves with the technique of multiple isomorphous replacement (MIR,
descrrbed m Chapter 6), or by using a smgle heavy-atom derrvatrve and the
multiple wavelength methods covered m Chapter 5
4. Once native X-ray diffraction data and phase mforrnatton are available,
then the electron density map is calculated and the chemical structure of
the macromolecule fitted mto the electron density map using a computer
graphics system, and refinement may begin. In refinement, the best fit
between the X-ray dtffraction data and the fitted model IS achieved
computatronally, etther using the more traditional techmque of conlugate
gradtent energy mimmrzatton dtscussedm Chapter 9 by Eric Westhof and
Phtlhppe Dumas, or by using the recent technique of molecular dynamtcs
discussed m Chapter 10 by Axe1 Brunger.
1.4. Diffraction Theory
This section shall discuss diffraction theory. The reader may wish to
skip this section on a first reading.
Most crystallographic computer programs use as input the structure
factor amplitudes Fhkl. These structure factor amplitudes are proportronal
to the square roots of the intensities (I), 1 Fhkl 1 = @&&TJ where L IS