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Hi Ian, and thanks for the interesting email.
The insect example should be understood in the context of the OED definition of resolution, which uses the word “measureable.” If one has a megapixel image
of a blurred-wing insect, the wings are certainly “measureable” in principle, but are in reality—in their nature—blurry. This is because, as you pointed out, the time-resolution is not good enough. The spatial resolution, however, is certainly good enough.
I would think, therefore, that it is somewhat misleading to estimate the resolution of the image based on not being able to see the wings.
That example, however, is perhaps not the best, since it’s complicated by involving time.
A simpler example, perhaps, would be of something which is inherently blurry even at one instant, say a protein diffracting in crystalline form. Since the structure
is averaged over many unit cells, the average structure is inherently blurry in different places (especially in bulk sovent!), which is what the ADPs/occ’s model. Even if I had a radiation-proof crystal with infinitesimal mosaicity, and could see spots at
0.5 angstroms, the blurry parts would remain blurry, even though the resolving power of the experiment would certainly imply being able to distinguish atoms.
Perhaps an even more plain example: image a megapixel image of a completely-white featureless surface. I cannot see anything distinct in the image, but I know
that if there were two black dots of a certain spatial separation, I would be able to distinguish them. If there are actually no dots, does that mean my resolution is nil? Or if there were dots, does it make sense to say that the local resolution around the
dots be vastly better than in the blank parts? I don’t think so.
Therefore I favor thinking of resolution in this conditional sense: under the current imaging setup, what separations would I be able to distinguish, if there
were ideal features there to image?
The cryo-EM definition of local resolution does not seem to fit this definition, and I remain unsure why they use this metric. Perhaps I will do a little reading
and talk to some experts around here.
JPK
From: CCP4 bulletin board [mailto:[log in to unmask]]
On Behalf Of Ian Tickle
Sent: Tuesday, March 07, 2017 10:27 AM
To: [log in to unmask]
Subject: Re: [ccp4bb] [EXTERNAL] Re: [ccp4bb] B-factors/Occupancies Versus "Local Resolution"
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 <[log in to unmask]> 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:[log in to unmask]] On Behalf Of Ian Tickle
Sent: Tuesday, March 07, 2017 9:02 AM
To: [log in to unmask]
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 <[log in to unmask]> 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