Structure studies of a protein:
macromolecular crystallography
(3D- structure) and Circular
Dichroism (secondary structure)
X-ray crystallography - is a
method of determining the arrangement of
atoms within a crystal, in which a beam of
X-rays strikes a crystal and diffracts into
many specific directions. From the angles
and intensities of these diffracted beams,
can be produced a three-dimensional
picture of the density of electrons within
the crystal. From this electron density, the
mean positions of the atoms in the crystal
can be determined, as well as their
chemical bonds, their disorder and various
other information.
X-ray crystallography is a form of elastic
scattering; the outgoing X-rays have the
same energy, and thus same wavelength, as
the incoming X-rays, only with altered
direction. A regular array of scatterers
produces a regular array of spherical
waves. Although these waves cancel one
another out in most directions through
destructive interference, they add
constructively in a few specific directions,
determined by Bragg's law:
d is the spacing between diffracting planes,
θ is the incident angle, n is any integer, and
λ is the wavelength of the beam
These specific directions appear as spots
on the diffraction pattern called reflections.
X-rays range in wavelength from 10 to
0.01 nanometers; a typical wavelength
used for crystallography is 1 Å (0.1 nm),
which is on the scale of covalent chemical
bonds and the radius of a single atom. Xray
sources diffractometer (anode from Mo
or Cu) and synchrotron.
Crystallization - Small-molecule and
macromolecular crystallography differ in
the range of possible techniques used to
produce diffraction-quality crystals. Small
molecules generally have few degrees of
conformational freedom, and may be
crystallized by a wide range of methods,
such as chemical vapor deposition and
recrystallization. By contrast,
macromolecules generally have many
degrees of freedom and their crystallization
must be carried out to maintain a stable
structure.
Three methods of preparing macrocrystals,
A: Hanging drop. B: Sitting drop. C:
Microdialysis
Protein crystals are almost always grown
in solution. The most common approach is
to lower the solubility of its component
molecules very gradually; if this is done
too quickly, the molecules will precipitate
from solution, forming a useless dust or
amorphous gel on the bottom of the
container. Crystal growth in solution is
characterized by two steps: nucleation of a
microscopic crystallite (possibly having
only 100 molecules), followed by growth
of that crystallite, ideally to a diffractionquality
crystal. The solution conditions that
favor the first step (nucleation) are not
always the same conditions that favor the
second step (subsequent growth). The
crystallographer's goal is to identify
solution conditions that favor the
development of a single, large crystal,
since larger crystals offer improved
resolution of the molecule. Consequently,
the solution conditions should disfavor the
first step (nucleation) but favor the second
(growth), so that only one large crystal
forms per droplet. If nucleation is favored
too much, a shower of small crystallites
will form in the droplet.
It is extremely difficult to predict good
conditions for nucleation or growth of
well-ordered crystals. In practice,
favorable conditions are identified by
screening; a very large batch of the
molecules is prepared, and a wide variety
of crystallization solutions are tested.
Hundreds, even thousands, of solution
conditions are generally tried before
finding the successful one. The various
conditions can use one or more physical
mechanisms to lower the solubility of the
molecule; for example, some may change
the pH, some contain salts or chemicals
that lower the dielectric constant of the
solution, and still others contain large
polymers such as polyethylene glycol that
drive the molecule out of solution by
entropic effects. It is also common to try
several temperatures for encouraging
crystallization, or to gradually lower the
temperature so that the solution becomes
supersaturated. These methods require
large amounts of the target molecule, as
they use high concentration of the
molecule(s) to be crystallized. Due to the
difficulty in obtaining such large quantities
(milligrams) of crystallization grade
protein, robots have been developed that
are capable of accurately dispensing
crystallization trial drops that are in the
order of 100 nanoliters in volume. This
means that 10-fold less protein is used perexperiment
when compared to
crystallization trials setup by hand (in the
order of 1 microliter).
The growing crystals are generally held at
a constant temperature and protected from
shocks or vibrations that might disturb
their crystallization. Impurities in the
molecules or in the crystallization solutions
are often inimical to crystallization.
Conformational flexibility in the molecule
also tends to make crystallization less
likely, due to entropy. Crystals can be
marred by twinning, which can occur when
a unit cell can pack equally favorably in
multiple orientations; although recent
advances in computational methods may
allow solving the structure of some
twinned crystals.
Measurment and Data collection: In an
X-ray diffraction measurement, a crystal is
mounted on a goniometer (fig. 1) and
gradually rotated while being bombarded
with X-rays, producing a diffraction
pattern of regularly spaced spots known as
reflections. The two-dimensional images
(fig. 2) taken at different rotations are
converted into a three-dimensional model
of the density of electrons within the
crystal using the mathematical method of
Fourier transforms, combined with
chemical data known for the sample.
Fig. 1
Fig. 2
The intensities of these reflections may be
recorded with photographic film, an area
detector or with a charge-coupled device
(CCD) image sensor. To collect all the
necessary information, the crystal must be
rotated step-by-step through 180°.
However, if the crystal has a higher
symmetry, a smaller angular range such as
90° or 45° may be recorded.
Data analysis: Each spot corresponds to a
different type of variation in the electron
density; the crystallographer must
determine which variation corresponds to
which spot (indexing), the relative
strengths of the spots in different images
(merging and scaling) and how the
variations should be combined to yield the
total electron density (phasing). A
byproduct of indexing is to determine the
symmetry of the crystal, i.e., its space
group (fig. 3).
Fig. 3
Model building and phase refinement
The intensity of each diffraction 'spot' is
recorded, and this intensity is proportional
to the square of the structure factor
amplitude. The structure factor is a
complex number containing information
relating to both the amplitude and phase of
a wave. In order to obtain an interpretable
electron density map, both amplitude and
phase must be known. The phase cannot be
directly recorded during a diffraction
experiment: this is known as the phase
problem. Initial phase estimates can be
obtained in a variety of ways:
• Ab initio phasing or direct
methods - This is usually the
method of choice for small
molecules (<1000 non-hydrogen
atoms), and has been used
successfully to solve the phase
problems for small proteins.
• Molecular replacement - if a
related structure is known, it can be
used as a search model in
molecular replacement to determine
the orientation and position of the
molecules within the unit cell.
• Anomalous X-ray scattering
(MAD or SAD phasing) - the X-ray
wavelength may be scanned past an
absorption edge of an atom, which
changes the scattering in a known
way. The most popular method of
incorporating anomalous scattering
atoms into proteins is to express the
protein in a media rich in selenomethionine,
which contains
selenium atoms.
• Heavy atom methods (multiple
isomorphous replacement) - If
electron-dense metal atoms can be
introduced into the crystal, direct
methods or Patterson-space
methods can be used to determine
their location and to obtain initial
phases. Such heavy atoms can be
introduced either by soaking the
crystal in a heavy atom-containing
solution, or by co-crystallization.
Having obtained initial phases, an initial
model can be built. This model can be used
to refine the phases, leading to an
improved model, and so on. Given a model
of some atomic positions, these positions
and their respective Debye-Waller factors
(or B-factors, accounting for the thermal
motion of the atom) can be refined to fit
the observed diffraction data, ideally
yielding a better set of phases. A new
model can then be fit to the new electron
density map and a further round of
refinement is carried out. This continues
until the correlation between the diffraction
data and the model is maximized. The
agreement is measured by an R-factor
defined as
A similar quality criterion is Rfree, which is
calculated from a subset (~10%) of
reflections that were not included in the
structure refinement. Both R factors
depend on the resolution of the data. As a
rule of thumb, Rfree should be
approximately the resolution in Ångströms
divided by 10; thus, a data-set with 2 Å
resolution should yield a final Rfree ~ 0.2.
Circular dichroism (CD) refers
to the differential absorption of left and
right circularly polarized light (fig. 4). This
phenomenon is exhibited in the absorption
bands of optically active chiral molecules.
CD spectroscopy has a wide range of
applications in many different fields. Most
notably, UV CD is used to investigate the
secondary structure of proteins. UV/Vis
CD is used to investigate charge-transfer
transitions. Near-infrared CD is used to
investigate geometric and electronic
structure by probing metal d→d
transitions. Vibrational circular dichroism,
which uses light from the infrared energy
region, is used for structural studies of
small organic molecules, and most recently
proteins and DNA.
Fig. 4
Circular polarization of light
-Electromagnetic radiation consists of an
electric and magnetic field that oscillate
perpendicular to one another and to the
propagating direction. While linearly
polarized light occurs when the electric
field vector oscillates only in one plane and
changes in magnitude, circularly polarized
light occurs when the electric field vector
rotates about its propagation direction and
retains constant magnitude. Hence, it forms
a helix in space while propagating. For left
circularly polarized light (LCP) with
propagation towards the observer, the
electric vector rotates counterclockwise.
For right circularly polarized light (RCP),
the electric vector rotates clockwise.
When circularly polarized light passes
through an absorbing optically active
medium, the speeds between right and left
polarizations differ (cL ≠ cR) as well as
their wavelength (λL ≠ λR) and the extent to
which they are absorbed (εL≠εR). Circular
dichroism is the difference Δε ≡ εL- εR.
The electric field of a light beam causes a linear
displacement of charge when interacting with a
molecule (electric dipole), whereas the magnetic
field of it causes a circulation of charge (magnetic
dipole). These two motions combined cause an
excitation of an electron in a helical motion, which
includes translation and rotation and their
associated operators.
Elliptical polarized light (purple) is
composed of unequal contributions of right
(blue) and left (red) circular polarized
light.
This relationship is derived by defining the
ellipticity of the polarization as:
where
ER and EL are the magnitudes of the
electric field vectors of the rightcircularly
and left-circularly
polarized light, respectively.
When ER equals EL (when there is no
difference in the absorbance of right- and
left-circular polarized light), θ is 0° and the
light is linearly polarized. When either ER
or EL is equal to zero (when there is
complete absorbance of the circular
polarized light in one direction), θ is 45°
and the light is circularly polarized.
Although ΔA is usually measured, for
historical reasons most measurements are
reported in degrees of ellipticity. Molar
circular dichroism and molar ellipticity,
[θ], are readily interconverted by the
equation:
The CD may also be a function of
temperature, concentration, and the
chemical environment, including solvents.
In this case the reported CD value must
also specify these other relevant factors in
order to be meaningful.
Additives, buffers and stabilizing
compounds: Any compound which
absorbs in the region of interest (250 - 190
nm) should be avoided. A buffer or
detergent or other chemical should not be
used unless it can be shown that the
compound in question will not mask the
protein signal. Therefore ensure that only
the minimum concentration of additives
are present in the protein solution.
Protein solution: The protein solution
should contain only those chemicals
necessary to maintain protein stability, and
at the lowest concentrations
possible. Avoid any chemical that is
unnecessary for protein stability/solubility.
The protein itself should be as pure as
possible, any additional protein or peptide
will contribute to the CD signal.
Contaminants: Unfolded protein,
peptides, particulate matter (scattering
particles), anything that adds significant
noise (or artifical signal contributions) to
the CD spectrum must be avoided.