On Monday 23 March 2009 14:34:24 Peter Zwart wrote:
> Hi,
> >
> > If we then require that the rms change in intensity be greater than the
> > average noise, then we can write down the requirement:
> > sigma(I_P) < rms(deltaI)
> >
> .
> > I_P/sigma(I_P) > 1.3*sqrt(MW/N_H)/fpp
>
> one can actually require that
>
> abs(delta I) > 3 sigma(delta I)
>
> Using eq. 13 from Acta Cryst. D61, 1437–1448, and the same (sometimes
> (very) questionable assumptions) James used, the magic factor 1.3
> inflates to 2.0
Please also have a look at
A Olczak, M Cianci, Q Hao, PJ Rizkallah, J Raferty, & JR Helliwell (2003).
"S-SWAT (softer single-wavelength anomalous technique)"
Acta Cryst. A59, 327-334.
in which the authors show several derivations for the estimated
anomalous signal, based on slightly different assumptions.
The web applet
http://skuld.bmsc.washington.edu/scatter/AS_signal.html
steers a more empirical course, lumping together various non-idealities
into a "pessimistic scenario" encompassing incomplete SeMet incorporation,
imperfectly tuned beamline, partial Met oxidation, etc.
> I once wrote a jiffy that allows one to simulate FOM's for various
> phasing + errors scenarios. I still have the code around, if someone
> is interested.
> Note that sometimes you cannot find sites, but with knowledge of the
> sites itself, phasing + density modification would result in
> interpretable maps (Acta Cryst. D60, 1085–1093).
> Also, the distribution of errors is rather important. I suspect that
> what matters in the end is that you have enough well-measured Bijvoet
> pairs to get the substructure. An empirical analysis possibly could
> shift the magic number back to 1.3 ;-)
>
> Cheers,
>
> P
>
>
> SAD Scientist ;-)
>
>
>
>
>
>
> > So, after doing these substitutions and rearranging, we get:
> >
> > sigma(I_P)/I_P < sqrt(2*N_H/(MW/14))*fpp/7
> > sigma(I_P)/I_P < 0.756*sqrt(N_H/MW)*fpp
> >
> > I_P/sigma(I_P) > 1.3*sqrt(MW/N_H)/fpp
> >
> > There are some obvious approximations here. Probably the biggest is
> > assuming that fpp = F_H. In actual fact, anomalous differences "count
> > double" since fpp contributes both to F+ and F-. I think Peter Zwart
> > pointed this out earlier. There is also another sqrt(2) in the opposite
> > direction because sigma(delta-I) is the quadrature sum of two sigma(I_P).
> > It also matters if you are interested in the rms anomalous difference or
> > the mean absolute anomalous difference, as these are not the same thing.
> > Nonetheless, I think this last formula should be accurate to at worst a
> > factor of two.
> > In general, it is a good idea to have your signal be more than equal to
> > noise, so I consider this formula a limit to be avoided rather than a goal
> > to be met. The skill and expertise required to solve the structure
> > increases quite sharply as your I/sigma(I) approaches this limit, but you
> > can always double I/sigma(I) by merging data from four crystals. The latter
> > is a better strategy.
> >
> > -James Holton
> > MAD Scientist
> >
>
--
Ethan A Merritt
Biomolecular Structure Center
University of Washington, Seattle 98195-7742
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