Hi Yong
Yes of course the _average_ resolution of the map, whether from single
crystal or PD, is determined 'more or less' by the minimum d-spacing
('resolution limit'), in the same way that the _average_ quality of the
agreement between the model and the data is related 'more or less' to the R
factor, but is that good enough? It tells you nothing at all about how the
resolution or the quality of fit of the model varies spatially over the
map. Also d_min need not be a single number as is traditionally claimed in
the vast majority of literature articles: there's no reason at all why it
shouldn't be anisotropic (varying with direction), though even this doesn't
tell you about the resolution as a function of position in the map.
Yes the resolution of the Patterson map obviously won't depend on the
model, but how often is the Patterson resolution useful in practice? I
think normally the width of the origin peak is more useful. I would say
the resolution of the ED or EM map is what interests most people.
My point about the difference between the meaning of resolution as used in
single-crystal MX compared with other fields is that MX is the only field
AFAIK where 'resolution' is frequently used in the way it is, i.e. as a
reciprocal space property of individual reflexions. We already had for
many years (in fact since Bragg proposed his famous law!) the concept of
d-spacing and d_min. In all other disciplines that use imaging, resolution
is a property of the image (which could of course be a diffraction image),
period. Using the same word with two different meanings only confuses
people, particularly when we already had a perfectly good word!
Cheers
-- Ian
On 7 March 2017 at 14:49, Yong Wang <wang_yon...@lilly.com> wrote:
> Ian,
>
>
>
> Won’t the spatial resolution of the electron density map be determined
> more or less by the “resolution” (d-spacing)? While the normal electron
> density includes model contribution, what about the resolution of the
> Patterson map? For the case of powder diffraction, after the lines are
> resolved, won’t the spatial resolution of the Fourier synthesis still
> depend on the d-spacing resolution limit? I don’t see much difference of
> the resolution used in crystallography from those used in other fields.
>
>
>
> Cheers,
>
>
>
> Yong
>
>
>
> *From:* CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] *On Behalf Of *Ian
> Tickle
> *Sent:* Tuesday, March 07, 2017 9:02 AM
> *To:* CCP4BB@JISCMAIL.AC.UK
> *Subject:* [EXTERNAL] Re: [ccp4bb] B-factors/Occupancies Versus "Local
> Resolution"
>
>
>
>
>
> Hi Jacob
>
> I'm a bit puzzled that you say that what you call 'local resolution' is
> used 'to model disordered regions' in cryo-EM. AFAIK it does no such
> thing: resolution is certainly used as a _metric_ of the EM map quality but
> it's not used for modelling. High resolution EM maps (which I assume is
> what we are talking about) are modelled in exactly the same way as X-ray
> maps, i.e. using an atomic model with co-ordinates, occupancies and B
> factors. Also I don't understand what you are saying about the insect
> wings: if they are blurred how can you 'see the wings' the same as you
> would stationary wings?, i.e. how can they have the same resolution as
> stationary wings, unless of course you change the experiment and stop the
> motion somehow (e.g. by using high-speed photography, but then note that
> greatly reducing the exposure time per image will also reduce the
> signal/noise ratio).
>
> Blurring (aka thermal motion or disorder) means 'loss of resolution',
> since if objects are moving or disordered the distance at which they can be
> distinguished as separate will clearly increase. So places in an electron
> density or EM map where atoms have moved over the exposure time of the
> experiment or are disordered (positioned differently in different unit
> cells or particles used in the averaging) will vary in resolution. This
> suggests that it might indeed be useful to analyse the variation of
> resolution in ED maps as is done in EM maps.
>
>
> I think part of the problem is that there's a good deal of confusion
> amongst MX practitioners in particular over the meaning of 'resolution'.
> The OED at least is very clear what it means: 'The smallest interval
> measurable by a telescope or other scientific instrument; the resolving
> power.'. This is precisely what it means in the overwhelming majority of
> scientific disciplines that make use of imaging (astronomy, EM, seisomology
> etc), and is also the definition you will find in all textbooks on optics
> and imaging in general.
>
> However macromolecular crystallography seems to be the one exception,
> where for example the descriptor 'resolution' in the MX literature is
> frequently ascribed to individal X-ray reflexions when what is meant is
> 'd-spacing' (or something directly related to that such as the magnitude of
> the scattering vector d*). This makes absolutely no sense! - resolution is
> the property of an _image_, which in the case of MX means the electron
> density map (or electric potential map in cryo-EM). This means that X-ray
> resolution depends on the model as well as the data, since the resolution
> is a property of the ED map, the map depends on the amplitudes and phases,
> the amplitudes depend on the data and the phases depend on the model. The
> situation is of course different in cryo-EM where the map is obtained
> directly from the data (which effectively contains both amplitude and phase
> information), so unlike the situation with X-ray maps, EM resolution has no
> dependence on the model.
>
> If resolution means anything in an X-ray diffraction pattern, it means the
> minimum distance on the detector between adjacent spots at which the spots
> are seen as separate, i.e. no spot overlap. This is in fact precisely the
> (correct) meaning that is routinely used in powder diffraction (
> http://www.ccp14.ac.uk/solution/resolution_powder_diffraction.html), i.e.
> the minimum separation of lines in the pattern that can be distinguished;
> it has nothing whatever to do with the minimum d-spacing of the lines in
> the pattern. There's really no good reason for MX to be so out of line
> with all other imaging techniques in this regard!
>
> Note that the accepted definition implies that resolution may be a
> function of position, so there is no reason in general to believe that it
> will have the same value everywhere even in a single image, so we should
> not make that assumption either explicitly or implicitly. The
> single-valued 'resolution limit' (minimum d-spacing), derived from the data
> immediately after processing and which is always quoted in the literature,
> is only an estimate of the average resolution, much like the R factor is an
> estimate of the average overall agreement between the data and the model,
> which tells you nothing about the magnitude of departures from the
> average. You need to look at the local metrics of agreement between the
> model and the electron density to get the full picture of the variation:
> similarly you need to look at the map to get the full picture of the
> variation of resolution. You can of course go to a multi-valued resolution
> limit, e.g. 6 parameters to describe it with an ellipsoid, or many
> parameters to describe it in terms of a fully general anisotropic surface.
> However this still does not address the fundamental problem that the
> resolution is a property of an image (map) which can vary with position in
> that image.
>
> Just my 2p's worth!
>
> Cheers
>
> -- Ian
>
>
>
>
>
> On 6 March 2017 at 19:54, Keller, Jacob <kell...@janelia.hhmi.org> wrote:
>
> Dear Crystallographers (and cryo-EM practitioners,)
>
>
>
> I do not understand why there is a discrepancy between what
> crystallographers use to models disordered regions (b-factors/occupancies)
> and what the cryo-EM world uses (“local resolution.”) I am tempted to say
> that “local resolution” is a misnomer, since I have been trained to think
> of resolution as a simple optical or physical characteristic of the
> experiment, and things that are blurry can in fact be “resolved” while
> disordered—one might think of the blurred wings of an insect in a
> long-exposure photograph, in which the resolution is of course ample to see
> the wings—but is there a good reason why the two different terms/concepts
> are used in the different fields? Could crystallographers learn from or
> appropriate the concept of local resolution to good benefit, or perhaps
> vice versa? Anyway, if there is a good reason for the discrepancy, fine,
> but otherwise, having these different measures prevents straightforward
> comparisons which would otherwise be helpful.
>
>
>
> All the best,
>
>
>
> Jacob Keller
>
>
>
>
>
>
>
>
>
>
>
