## what is the phase problem? x ray crystallography

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benny
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### what is the phase problem? x ray crystallography

hey people.. can anyone give a succint definition of the phase problem in x ray crystallography? we've started looking at it in our course, but it hasn't really been defined. i've looked high and low on the web as well, but i have been unable to find any decent definition. also,, why is it a problem, in terms of determining protein structure? obviously it is, but i'm not sure why.
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blcr11
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In order to calculate electron densities from a diffraction experiment you need three pieces of information, only two of which can be determined directly by the experiment. Those three things are the indicies of a reflection (h,k,l), the intensity of the reflections, I(hkl), and the phase angles of the reflections, α(hkl). Now the indices of a reflection will be determined by the symmetry of the crystal and by convention, and the intensities can be measured by some detection device: a photon counter of some sort, a piece of film, or an image plate, or ccd, for example. The phase of a reflection is analogous to phase differences between sine or cosine waves or the diffraction of photons in a double-slit experiment, and comes from the interference between radiation diffracted by different hypothetical planes within the crystal (see a discussion of Bragg’s Law). You need the phases of the reflections in order to caluclate the electron density within the crystal, but you can’t determine them simply by measuring the I(hkl)s. You have to do something more. Therefore, the phase problem refers to this doing “something extra” to somehow extract phase information from the diffraction experiment.

Once you have estimates of the intensities and phases of the reflections, you can calculate the electron density within the crystal and build a model by placing atoms into density as appropriate. To see how well your model explains the data, you “back” calculate the diffraction pattern you expect to see, given your model, and compare it to the diffraction you actually see. By cycling back and forth between structure factors and electron densities (by fourier and inverse fourier transformations) you gradually build a better model that (hopefully) explains more and more of the diffraction, until finally you decide you can’t improve the model any further with the data in hand, and you stop, saying, “Here is the crystal structure of…”

blcr11
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These are perhaps more than you want.

http://www.ruppweb.org/Xray/101index.html

http://www.mineralogie.uni-wuerzburg.de ... /teaching/

http://www.ysbl.york.ac.uk/~cowtan/sfap ... intro.html

The “phase problem” is a problem for both small molecule and protein structures, but it’s a little more of a problem for proteins as there aren’t so many ways to derive the phases, and the resolution of the data usually aren’t as good—typically 2-3 angstroms resolution for proteins compared to 0.7-1 angstroms for a routine small molecule crystal structure. Nowdays, most small molecules can be solved by direct, ab initio methods using only the intensity data and formalized chemical intuition. Direct methods are possible for protein structures, but it gets harder to apply the method as the number of atoms in the unit cell gets larger and the resolution of the data gets worse.

benny
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### xray crystallography

thanks very much for that. it clears things up a great deal.
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mcar
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Proteins vary in every nature. Specificity is suggested to be reliable in terms of identifying, sorting, isolating (and the like) proteins.

Compare I think, isolation of protein techniques with that of x-ray crystallography.
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