Phase ambiguity problem

The phase ambiguity problem can also be understood from the mathematical expression shown next. We can express the protein phase angle ap from the following equation. 

In order to resolve the phase ambiguity from the first heavy-atom derivative, the second heavy atom must bind at a different site from the first. If two heavy atoms bind at the same site, the phases of will be the same in both cases, and both phase determinations will provide the same information. This is true because the phase of an atomic structure factor depends only on the location of the atom in the unit cell, and not on its identity (Chapter 5, Section III.A). In practice, it sometimes takes three or more heavy-atom derivatives to produce enough phase estimates to make the needed initial dent in the phase problem. Obtaining phases with two or more derivatives is called the method of multiple isomorphous replacement (MIR). This is the method by which most protein structures have been determined. 

The structure factor is now a real function, but a phase ambiguity of either 0 or 2ir still exists. Without this information Fourier synthesis cannot be performed directly. Crystallographic analysis consists of strategies to overcome this phase problem. 

Here we have two possible signs for p, because we have an arccosine function, which gives two possible solntions for a single argument. Thus, the phase ambiguity is actually a mathematical problem. 

Because we get one true phase and one false phase, we do not know which one is the correct one to choose. Thus, the next step in the isomorphous replacement method is to resolve the phase ambiguity. Although the phase ambiguity is a mathematical problem, most crystallographers routinely solve it by collecting more experimental data. 

Fig. 3 Important 19F-labelled amino acids, (a) Compounds that are wo-steric to native amino acids can be incorporated into proteins biosynthetically, but they possess too many degrees of torsional freedom to be useful for ssNMR structure analysis, (b) In these artificial amino acids the 19F-reporter group is rigidly attached to the peptide backbone. They can be incorporated by solid-phase peptide synthesis, but some problems can arise due to racemisation (4F-Phg, 4CF3-Phg), steric hindrance of coupling (F3-Aib) or HF elimination (fluoro-Ala, F3-Ala). 4F-Phg is additionally problematic due to an ambiguity of the side-chain rotamer. The preferred 19F-labels for ssNMR structure analysis are CF3-Bpg and CF3-Phg (as suitable substitutes for Leu, lie, Met, Val and Ala), as well as F3-Aib and CF3-MePro...

The problems of directional ambiguity and sensitivity fading can be overcome by a phase modulation of the light source. If the branches are not identical or the splitting or combining of the beam is imperfect, then the MZl system has to be calibrated and an offset value measuring the blank determined A(p = Acp + Ameasured value and as offset value. 

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