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 Positivity and improved resolution

Given that the maximum entropy map is the most uniform map consistent with the data, it is surprising how much more informative can be from the conventional Fourier synthesis, especially when accurate data are available. The following figure illustrates this point by comparing a conventional 15Å low resolution projection map with the corresponding GraphEnt map, and with two conventional maps calculated at higher (13 and 11Å) resolution7.

Figure: Projection GraphEnt map
Low resolution example

There are several things to note in these maps : The first is that the GraphEnt map is always positive with almost no detail in the background. This is clearly not the case with the Fourier syntheses, which have negative regions (dashed lines) and fine detail in the background which arise not only from the absence of the F000 term, but also from the series termination errors8. The second observation is that the peaks on the MAXENT map are better resolved, even when compared with the 11Å Fourier synthesis. This is not too surprising given that the Fourier transform of the maximum entropy map has non-zero amplitudes all the way to physical limits of the transform.


... resolution7
The asymmetric unit of the pmg plane group consists of the projections of two lysozyme molecules related by a simple translation.
... errors8
In all maps shown, contours are plotted every 10% of the maximum density.

next up previous contents
Next:  Insensitivity to missing data Up:  Examples Previous:  Examples   Contents
NMG, Nov 2002