If you treat the amplitude and phase as a complex number and follow
the math I believe it turns out that real space and reciprocal space
refinement are identical... If there are no uncertainties.
Any model of the uncertainties can also be expressed in either space,
but a model that is simple in one space is very complicated in the
other. The simple case we live with of a (nearly) Gaussian uncertainty
in the amplitude and a HL uncertainty in phase angle transforms to
an uncertainty in real space where every density point is correlated
to every other point to some degree or another. A simple constraint
in real space, such as the flatness of bulk solvent, results in an
uncertainty model in reciprocal space that has correlations between
each pair of structure factors.
Reciprocal space refinement has been so successful over the years
because the model that the uncertainties of each structure factor being
independent of all the others is pretty close to being true. Of course
when your phases are derived from a heavy atom model errors in the model
will cause correlated uncertainties in your phases which are currently
ignored. This is one reason why refining with phases is more problematic
than refining with amplitudes alone, despite the fact that we can
weight the phase information much better than in the past.
I have not been following the uncertainty models in modern real
space refinement programs and can't comment on why they give better
results in some circumstances. I presume this is because the uncertainty
for the information about density maps that is being restrained can
be expressed more simply in real space than reciprocal space.
Dale Tronrud
Anastassis Perrakis wrote:
> On 10 Aug 2007, at 18:59, Pavel Afonine wrote:
>
>> Hi Mike,
>>
>> the best is to do both in a loop:
>>
>> for cycle in cycles:
>> - do real space refinement;
>> - do reciprocal space refinement
>
> Well - thats what we all do - right ?
> The real space refinement can be done either with the tools from Chapman
> at al,
> or interactively by the user or by (here I go again ... ) ARP/wARP or
> Resolve etc etc.
> In all cases we fit the model to the map ... only the tools differ.
>
> Although I would be tempted to suggest some general reading to Mike
> [log in to unmask] [1]
> (there is one copy of Blundell and Johnson available at Amazon for
> 1239.64$, quite a bargain)
> the most simple minded way to think of it is that in real space you fit
> a piece of model to a piece
> of density locally. In reciprocal space the data from the entire
> molecular model is fitted
> to the entire diffraction dataset at the same time. The argument about
> phases I think you know it,
> so I will not diatribe on this. ;-)
>
> Also, there are no more than 2-3 MAD experimental phase-sets out there
> (all in very high resolution)
> that can claim that the phases derived from them are as accurate as the
> phases from the refined model.
> Thus even if you let aside all of the rest of the theory, the phases we
> 'measure' these days are not that good.
>
> Also, usually we think of 'excellent' phases that come from density
> modification. Thats already modeling ...
>
> Finally, I think the vast majority of structures are still from
> molecular replacement, and thus you don't have good phases by definition.
>
> A.
>
> [1] Why don't people subscribe to ccp4 from their real institute email
> addresses ?
>
> PS Is nobody reading Nature these days or no-one likes a good argument
> about crystallographic models any more in this bb ?
>
>
>>
>> Have a look at this very nice paper:
>>
>> Acta Cryst. (1999). D55, 835-845 Critical initial real-space
>> refinement in the structure determination of arginine kinase
>> G. Zhou, T. Somasundaram, E. Blanc, Z. Chen and M. S. Chapman
>>
>> and other "real space refinement" related papers by M. S. Chapman et al.
>>
>> Pavel.
>>
>> Mike S wrote:
>>> Dear CCP4 experts,
>>>
>>> Recently, I was debating a colleague on the pros/cons of refinement
>>> done in reciprocal space compared to refinement in real space.
>>> I always thought reciprocal space refinement was preferable since
>>> measured amplitudes will be more accurate than calculated phases
>>> (unless good experimental phases are available). My colleague argued
>>> that with sigmaA and maximum-likelihood methods, calculated phases
>>> are much "better" than they were in the past and the two refinement
>>> techniques are equivalent in terms of robustness. He said the reason
>>> most software hasn't switched entirely to real-space refinement is
>>> due to computational issues.
>>>
>>> Please help enlighten me. All comments/diatribes welcome.
>>>
>>> Thanks,
>>> Mike
