Re: What is the phase problem in synchrotron analysis of X-ray diffractions?

Dear User,

The question which you ask has to do with determination of structures
using all diffraction techniques, not just the synchrotron. Diffraction
patterns obtained on a synchrotron are not at all different from those
obtained on laboratory sources, such as rotating anode or a sealed tube.
There are several points which make synchrotron radiation desireable,
though. These are:

Intensity (typically 1000 - 100000 times brighter than lab sources)
Linearity of the beam (angular divergence of a synchrotron beam is much
less than that of lab systems)
Tuneable wavelength (lab sources are quantized in terms of orbital
energies and depend on anode material - copper, molibdenum, silver K
alpha wavelengths are typical whereas synchrotron radiation is tuneable
smoothly)

The single point on an area detector or image plate does not reveal ANY
phase information. Moreover, in order to obtain a single peak, many
points have to be averaged and brought together in three dimensions, to
obtain a peak profile. Still, each *reflection* (diffraction peak) does
not carry ANY phase information. This situation would be different if we
had x-ray lasers or if we could measure phase AND amplitude at the same
time - the latter is forbidden by Schroedinger's principles though).

So, how is the phase problem solved ? Well, as you probably know, there
are several methods available, including:

direct methods
multiple or single isomorphous replacement (MIR/SIR)
multiple or single anomalous replacement (MAD/SAD)
and of course, molecular replacement (MR).

The above four methods are the most used to-date.

Relatively small structures (up to 1000 atoms or so) are routinely solved by 
direct methods. Nowadays, large structures can be also solved
directly (it's still quite difficult), provided that the high-resolution
data ( 1.1 A or so) are available.
Multiple/single isomorphous replacement is a 'trick' played on the
protein crystals in order to deduce phases. Crystals of macromolecules
are soaked in solutions containing reactive heavy atom compounds.
Diffraction data from non-derivatized crystals and from derivatives are
compared and the positions of heavy atoms are derived from Patterson
maps (as you probably know, Patterson function does not use phases).
Then, knowing the position of heavy atoms, phases can be deduced from
the differences in intensities of the reflections from 'native' and
'derivative' datasets. This method is probably historically the most
useful one.

MAD has to be performed on a synchrotron or some other source of
tuneable radiation. In addition, MAD/SAD requires that anomalous
scatterers were present in the structure. This methods takes into
account the fact that anomalous scatterers can be located in the
structure using Patterson maps. Then, knowing the positions of these 
scatterers, their contributions to the intensities of the peaks can be
calculated and phase information may be derived from these
contributions, using an iterative process. Several wavelengths are
usually needed for decent phasing, however, if the structure is well
ordered and the data is of high quality and is available to high enough
resolution, one wavelength may suffice. For large structures, such as
macromolecules, the number of anomalous scatterers and the 'power' of
each scatterer should be large enough. For example, 1 selenium can phase
about 30-60 protein residues whereas one mercury can phase up to 650
residues.

MR is basically an attempt to use previously solved structure as an
incomplete model for the unknown structure, in order to obtain initial
phases. This method only works if there is sufficient degree of
similarity between the unknown and the known structures.

I cannot relay in this short answer all the principles behind these
methods. I cannot provide web references right away because our WWW
access is disrupted as of right now. Hence, I urge you to look up keywords 
such as 'molecular replacement' or 'multiple anomalous
diffraction' etc. using altavista or metacrawler. There is a number of
excellent tutorials available on the web. I also invite you to write me
with more specific questions - after all, X-ray (and neutron)
diffraction studies is what I do for living.

Best regards,

A.G.E.