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
