Re: [ccp4bb]: simulation of averaging effect?

[Edward Berry <eaberry@lbl.gov>]

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Dear JingHua,
I think this is complicated by the fact that iterative molecular averaging
as part of density modification does not simply average the structures,
but also changes the phases.

In applications such as spectroscopy, signal averaging increases the signal 
to noise ratio because adding in more spectra increases the signal
proportionately while the random error partially cancels and increases
proportional to the square root of N.

While a single cycle of molecular averaging may improve density by the 
same method, the real power comes from phase improvement. The phases 
are recalculated at the end of each cycle. It has been shown that this 
amounts to applying an iterative real space method to solve the 
MR equations, i.e. find phases that are consistent with (a) the observed 
amplitudes and (b) the NCS symmetry operators. If the NCS really does 
apply, this gives improved phases and the density is better, 
even in the final fft map without averaging. 

If part of the asymmetric unit does not obey the NCS, The contribution 
of that part to the phases will be worsened by averaging. This by 
itself would not be a problem, because density modification programs
allow you to define areas which are neither averaged nor flattened
but carried through without modification.

However if crystal packing is determined by the symmetrical capsid,
the genome will take on each of 60 (64?) different orientations with
equal probability (frequency, occupancy). I guess it is this averaging
which takes place during crystal packing, and not the averaging during 
density modification, that destroys the density of the non-symmetrical 
parts.  Thus given the averaged structure that exists in the crystal,
NCS applies everywhere, and it is correct to use an averaging mask 
which includes everything but solvent. The structure you obtain has
the genome averaged, not by the density modification but by the 
crystal packing. 

This could be simulated by calculating a map from 
an assumed structure, doing a single cycle of molecular averaging, 
and examining the averaged map. Use a program like the RAVE package 
which gives you access to the intermediate steps. However you can 
imagine what it would look like without doing the experiment- 
60 copies of the structure in different orientations, 
each at 1/60 occupancy. It would probably look a lot 
like solvent!

Ed

Jinghua Tang wrote:
> 
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> 
>  In virus crystallography, the 60 folds averaging is used to improve the
> structure which obey the strict icosahedral symmetry. Because of the
> crystal and symmetry averaging, the genome inside the virus is rarely
> visible.
> 
>   I am wondering if someone could suggest a way to simulate the averaging
> effect. If some real information is averaged with noise a couple of times,
> or 60 times, what would the initial object look like after averaging.
> 
>   Thank you very much for your wonderful suggestion!
> 
>   Jinghua