Phasing methods:
Multiwavelength anomalous
dispersion (MAD)
Lecture 10
02/15/06
Methods for phase determination
Molecular replacement (MR)
• Only one native crystal is needed. One homologous
structure must be available. Quick and simple.
Multiple isomorphous replacement (MIR)
• Use heavy atom to perturb diffraction intensities
Hg Pt
• At least one native crystal and two crystals soaked in
U
two heavy atom solutions must be available.
• Need no information about the unknown structure.
Multiwavelength anomalous dispersion (MAD)
Se
(S → Se)
• As X-ray wavelength approaching absorption edge,
anomalous scattering occurs – Friedel pairs are no
longer equal in intensities.
• Only one crystal is needed but multiple data sets must
be collected at three different wavelengths.
• Se-Met protein is usually needed. Excellent electron
density map.
Anomalous scattering
•
•
There is a sharp discontinuity in
the dependence of the absorption
coefficient on energy (wavelength)
at the energy corresponding to the
energy required to eject an innershell electron. The discontinuity is
known as an absorption edge.
For Cu, the K-absorption edge is
at 1.380Å.
K absorption
edge
– Compared to Kα at 1.5418Å
•
•
Near absorption edge, electrons in
an atom can no longer be
considered as free electrons. The
consequence is anomalous
scattering.
Heavy atoms (Hg, Pt, Se) are
common anomalous scatterers
because their absorption edges
fall within usable X-ray energy
ranges.
The atomic absorption coefficient for Cu
The energy of an photon is
E=hc/λ
When the incident photon has relatively low energy
•The photon is scattered, as it has insufficient energy to excite any of the
available electronic transitions.
•The scattering effect of the atom may be adequately described in using the
normal atomic scattering coefficient f0 only.
When the incident photon has high enough energy
• Some photons are scattered.
• Some photons are absorbed and re-emitted at lower energy (fluorescence).
• The scattered photon gains an imaginary component to its phase (f" scattering
coefficient becomes non-zero); i.e. it is retarded compared to a normally
scattered photon.
Anomalous scattering
For an anomalous scatterer, its scattering factor now becomes:
Anomalous scattering
• Regular scattering factor decreases as resolution increases
• But anomalous component is rather independent of resolution
because it is mainly caused by inner electrons.
Anomalous scattering factor for different atom
types
Anomalous scattering is mainly dependent on atom
types and wavelength
Anomalous Scattering breaks Friedel’s law
•
Friedel pairs
– Friedel pairs are Bragg reflections related by inversion through the
origin.
•
Friedel's Law
– Friedel's Law states that members of a Friedel pair have equal
amplitude and opposite phase.
•
Anomalous Scattering breaks the law
Protein only
Protein &
anomalous scatterers
Anomalous scatterers only
Anomalous Scattering breaks Friedel’s law
If we incorporate anomalous scattering, F(+) ≠ F(-). The center of
symmetry no longer holds any more.
Protein phase determination with anomalous
scattering - SIRAS
Three circles:
FP, FPH(+) and FPH(-)
α1 and α1’ are symmetric with
respect to the horizontal axis
because (hkl) and (-h,-k,-l)
have opposite phases.
Protein phases can be
determined from one native
data set and one derivative
with anomalous scattering
information (SIRAS).
Single isomorphous replacement with anomalous scattering (SIRAS)
Protein phase determination with anomalous
scattering - SIRAS
A mirror image is draw for FH(-)
One common intersection point
Multiple Wavelength Anomalous Dispersion
(MAD) method
MAD exploits the wavelength dependence of anomalous
scattering
Hendrickson pioneered the method, and
used MAD for solving the structure of a
protein in 1988.
The application of MAD in protein
crystallography is possible due to the
availability of tunable synchrotron
radiation
Multiple Wavelength Anomalous Dispersion
(MAD) method
MAD exploits the wavelength dependence of anomalous scattering
Data collected at three wavelengths,
Heavy atom derivatives can be prepared
by making Se-Met protein or heavy
atom soaking, etc.
Se
S, Ca or Cu found in some native
proteins are also weak anomalous
scatterers.
One Se atom (atomic number = 34) in a
150aa protein is sufficient for MAD
Choosing
wavelengths for
MAD data
collection
Se
Typically λ3 and λ4 are between
100eV and 1000eV from the
absorption edge.
The f’ and f’’ values need to be determined
experimentally
The Cromer/Liberman theoretical values for scattering factors are not
accurate for energies very near an absorption edge. The interaction of the
scattering atom with its chemical neighbors complicates the scattering
behavior considerably. The calibration of X-ray wavelength at different
beamlines is also a concern.
Cu site in single crystal of a blue copper protein [Guss et al, 1989].
X-ray fluorescence is measured for each crystal or
crystal type
Absorption edge
Anomalous scattering is most easily measured as a function of x-ray energy by
noting either the sharp increase in absorption or in fluorescence
The f’ and f’’ components can be derived
from the fluorescence absorption curve
Anomalous Patterson function
We define
∆F is the difference between the amplitudes of the structure
factor for the reflections (h,k,l) and (-h,-k,-l)
Patterson function calculated using coefficient ∆F is called
“anomalous difference Patterson”.
Data collected at whiteline (or peak wavelength) are often
used for map calculation.
It can be used independently or combined with isomorphous
difference Patterson to search for heavy atom positions.
The combined Patterson map boost signal by a factor of 2.
Heavy atom positions are determined from the
anomalous difference Patterson map
Anomalous difference Patterson is calculated with coefficients |∆F|2
The map is usually very
noisy, but computer
programs, such as SOLVE,
SHELXD, and SHARP, can
be used to locate heavy
atom sites using Patterson
maps.
u = 1/2 Harker Section
Algebraic processing of MAD data
Only λF is known
λF=
total observed scattering amplitude from our diffraction
measurement at wavelength, which has an unknown
phase
FT = Normal scattering component of all atoms
FA = Anomalous scattering contribution from all atoms
∆φ= Difference in phase angle between normal and
anomalous scattering components
Developed by Hendrickson and coworkers [1985], based
on the Karle’s treatment of the problem [1980]
Jerome Karle
(1918- )
• Each of our measurements of F(h) at some wavelength gives us one
instance of the equation above, and the separate instances may be treated
as a system of simultaneous equations from which we want to obtain the
quantities FA, FT, and ∆φ.
• One equation for F(h) and one for F(-h)
• Therefore at least two wavelengths are needed to solve the equations.
• φT = φA + ∆φ, where φT is the protein phase angle
MIR vs. MAD
• MIR
– Data are easy to collect at a single λ
– Several crystals are required
– Lack of isomorphism is common.
• MAD
– Data needed to be collected at multiple (often 3) λ’s
– More accurate data are required because anomalous
differences are relatively small and more prominent at
high resolution
– Only requires one crystal
– No non-isomorphism problem.