Thank you very much for this clear and long answer, Dale. You gave me exactly the information I needed.
Thanks again having taken the time to answer to my questions. Cheers. Peter On Thu, 5 Feb 2009 14:51:15 -0800, Dale Tronrud <det...@uoxray.uoregon.edu> wrote: > A map file stores a density value for each point on a grid. The > units and nature of that item is not defined in the format of the map. > A map can store any number of things. The actual values are defined > by the process that created the map file. > > For electron density maps you will find that some contain values > measured in e/A^3, others contain values that are normalized Z scores > (The standard deviation of the variation about the mean is set to > 1.0), or just a bunch of numbers with arbitrary and mysterious units. > > One tends to use e/A^3 when trying to relate the map to expected > electron density or to compare one map to another. A normalized map > is useful if you are interested in the frequency that a density value > of that magnitude appears in the map. (Is this value common or rare?) > One uses arbitrary values if one has an attachment to honesty. > > Calculating an electron density map in units of e/A^3 is not an > easy task. The diffracted intensities are not measured, themselves, > in "real" units. Their magnitude only has meaning as intensities > relative to the other intensities in the same dataset. For the map > to be expressed in units of e/A^3 the diffraction intensities must > be expressed in units of e/Unit Cell (at least that is the convention). > This is a hard problem and many papers have been written on the topic. > > If you have a well refined and complete model for the contents of > the crystal you can use the calculated diffraction pattern as a template > to scale the observed intensities and calculate maps in e/A^3, but > this is an approximation as no model is complete or completely correct. > > The other big issue is that we cannot measure the one reflection > that defines the average of the electron density in the crystal. It > happens to always hit the beamstop. Because of this problem our maps > usually have an average value of zero, which is of course wrong. Even > when the density values are expressed in e/A^3 the intention is that > each value in the map must have a number added to it to achieve the > true value at that point. At least it's the same number everywhere > in the map, although we don't know its value. > > Because of these issues and uncertainties, when maps are compared > they are usually compared using a correlation coefficient. The > correlation coefficient is relatively unaffected by these scaling > problems and will usually give the same answer when given any of > the kinds of maps I described. > > If you want a more detailed comparison of electron density values > you really have to get into the details of each of the datasets and > scaling that was applied to ensure that your results are meaningful. > > Estimating the error bars of an electron density map is another > enormous problem. As you would expect, it depends critically on the > origin of the map. The error analysis of a map calculated from MAD > phasing is quite different than that of a map calculated using a > refined model as a reference. > > One complication is that the error level is not necessarily the > same everywhere in the map. In addition the errors at different > regions of the map are not independent. The correlation of deviations > at different regions of the map are likely more important to any > analysis then any simple overall error bar. > > However, if you insist on an error level, my best guess would be > to identify the regions of bulk solvent and calculate the rms deviation > from the mean there. Since these regions should be flat, and deviations > from the mean must be due to something that does not represent election > density. We might as well call it "error". > > Dale Tronrud > > > Peter Schmidtke wrote: >> Dear CCP4BB List Members, >> >> first of all I am not a crystallographer, but I would like to get some >> things clear, things I did not find in "Crystallography Made Crystal >> Clear" >> and on the internet for now. >> >> I am trying to read electron density maps in the EZD format. These maps >> contain scaled values of electron density and size and shape of the unit >> cell. How can I convert the values of intensities (what is the unit of >> these values?) to the probabilities you can see in coot for example (1.03 >> electron / A^3), >> Once I have achieved this conversion, can I compare densities of >> different >> maps of different proteins? If not directly, is there a way to do so? >> >> Last, is there a way to know the experimental error made on intensity >> values of a map? >> >> Thanks in advance. >> >> -- Peter Schmidtke ---------------------- PhD Student at the Molecular Modeling and Bioinformatics Group Dep. Physical Chemistry Faculty of Pharmacy University of Barcelona
