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<mailto: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
