Re: [ccp4bb]: contour ?

[Ian J Tickle <i.tickle@mail.cryst.bbk.ac.uk>]

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On Wed, 5 Sep 2001, Gerard "DVD" Kleywegt wrote:

> - if you cut out maps around your molecule and then use
>   them in O, the "sigma level" is recalculated by O. As
>   a consequence, this level will almost always be lower
>   than the sigma level in the asymmetric unit, and features
>   will show up at deceptive levels (e.g., a "2-sigma"
>   peak may be just a 1-sigma noise feature). [This problem
>   does not occur when you use to good old map_* commands.]

Interesting discussion, keep it up!

Speaking from a statistical point of view, a couple of points are worth
making on the subject of calculating the standard uncertainty (SU) of the
electron density (or difference density).  Programs actually calculate the
RMS deviation from the mean of the electron density.  The question is, under
what conditions is this an unbiased estimate of the SU ? - this is really
what we are interested in if we want to judge the significance of peaks (or
troughs) in the density.  The answer is that the following conditions should
apply:

1. The sample of density points used must be independent, for example 2 or
more of the points used should not be related by the space-group symmetry.
This is pretty self-evident, nevertheless most programs which purport to
compute the RMS as an estimate of the SU violate this condition!  FFT does it
correctly since by default it always computes exactly one asymmetric unit (or
should do!).  However when you "extend" the a.u. to cover the volume of
interest, the chances are that some points will have symmetry mates in the
extended map.  The correct procedure would be to simply use the value of the
RMS originally computed by FFT.

2. The sample of density points used must either be the entire population or
a random sample of it.  Again the same argument as above applies here: it is
clearly not valid to use the RMS value for a selected non-random portion of
the a.u. as an unbiased estimate of the SU.

3. The sample of density points used must truly represent the "noise".  The
computed density will almost always include some of the "signal" we are
looking for (of course this will always be true in a Fo or 2Fo-Fc map, and
true for a Fo-Fc map except at completion of the structure).  Therefore
ideally the points containing signal+noise should be excluded from the
calculation - for difference maps this can be done by using only the linear
portion of the normal probability plot close to the origin to estimate the
SU, and excluding the curved portion which should mostly represent the signal
(assuming of course that the noise really does have a normal distribution).
This method only really works well if the map is mostly noise with a small
amount of signal - so it can only be used for difference maps.

How much effect these corrections will have on the estimate of the SU will
depend obviously on the ratio of the volume of the map used to that of the
a.u., and the ratio of the number of points containing some signal to those
containing only noise.

-- Ian Tickle (Astex Technology)