How To Evaluate Electron Crystallographic Data

Size: px

Start display at page:

Download "How To Evaluate Electron Crystallographic Data"

Moses Wilkins
5 years ago
Views:

1 How To Evaluate Electron Crystallographic Data Vinzenz Unger, Dept of Molecular Biosciences, Northwestern University Chemistry of Life Sciences Institute, Northwestern University

2 Unstained = Resolution Low dose electron images of frozen samples have very low contrast and do not reveal individual molecules. However, the calculated transforms show strong diffraction maxima

3 ~30Å Contouring: 2σ Membrane Domain

4 CTF-Plot for a Single Image

5 Projection Data: Not all Phase Errors Are Created Equal Question: How many images are required to obtain reliable projection data? phase error after averaging centric phase error black: gap junction 179,353,516,596 and 1266 measurements for 76 unique reflections, p6 symmetry grey: NhaA Na + /K + -antiporter (Williams et al 1999) 368, 713, 936,1152 and 1704 measurements for 204 unique reflections, p22121 symmetry

6 Averaging of data.. EXCERPT OF DATA FROM 3 DIFFERENT IMAGES H K ZSTAR AMP PHS All measurement are strong excellent S/N-ratio phase value is well defined and very close to expected target All measurement are strong excellent S/N-ratio phase value is well defined and very close to expected target This one is more interesting because there is some sort of correlation between the strength of the measurements and the closeness to the expected phase value These three examples illustrate two issues that need to be taken care of: In projection, data are averaged by calculating an amplitude weighted vector average. Each reflection will have an intrinsic phase error that globally reflects the goodness of the data points. Therefore, we can express the statistical significance of the average phase by listing the cosine of the phase-error associated with the average itself. This value is known as FOM (figure of merit) and is a number between either 0-1 (absolute) or (percent). While an average may be significant, it is likely to deviate by a certain amount from the exact target value (where applicable). Thus, if we want to enforce the symmetry, we need to impose the correct phase by rounding the experimental data to their theoretical values. This is a deliberate manipulation to make the data fit ( no matter what ) and therefore needs to be taken into account when assessing the overall reliability of the data.

7 Averaging of data..an example. Shown is a partial structure factor list obtained after averaging data from three independent images of the gap junction channel that serves as test sample for our purposes: H K L Amp Phase FOM Adjusted Adjusted phase FOM As expected, some of the averages are quite a bit off their expected targets. We can take care of it by treating the rounding off as an additional phase error. In this case, rounding will decrease the FOM depending on how much the phase deviates from the target. This is sensible because it acknowledges that, in some cases, the rounded phase value is only our best guess, and we don t want it to contribute to the structure calculation as much as the really well defined structure factors. How can one sensibly represent this abundance of information? Note on the side: so far, we only considered phases. However, in order to get the correct vector averages, the amplitudes need to be corrected for the impact of the CTF as well. In the single particle work, this is a very difficult issue. In 2D-crystallography, we can relax because we only need to get it approximately right (remember, the amplitude is contributing much less to the total structure then the phase = an error in amplitude is handled gracefully, an error in phase is deadly). In most cases we simply do the equivalent of dividing by the CTF, limiting the maximum scaling to 5x as we approach a zero in the CTF.

8 Being Truthful - And Comprehensive

9 B=0 B=-350 B=-680 enhances 110x at 6Å

12 Example for a Lattice Line

13 Figure 1 Amplitude and phase variations along higher resolution lattice lines after merging data from tilted crystals in the two-sided plane group p6. V M Unger et al. Science 1999;283: If shown: present lattice lines close to the claimed resolution cutoff don t show low resolution lattice lines.

14 PLTILTK plot for a connexin 43 data set (taken from(10)). The 60 wedge of the plot covers the spread of unique tilt geometries for the p6-plane group of the sample. The x-axis of the plot refers to the crystal tilt in degree. Each diamond corresponds to one specific image in the data set. Numbers inside the diamonds reflect the following quality criteria: 1 50% complete in bin between (4/3)r and r with r = resolution limit; 2 50% complete in bin between 2r and (4/3)r; 3 50% complete in bin between 4r and 2r; 4 50% complete in bin between and 4r; 5 does not meet quality criterion in any resolution bin perpendicular to tilt axis. Images with an IMQ of 5 should be excluded from the data set. Diamonds separated by more than κ 50 represent images that have less than 50% overlap in their data perpendicular to the tiltaxis. Diamonds separated by more than κ 0 refer to images that have no data overlap perpendicular to the tiltaxis

There and back again A short trip to Fourier Space. Janet Vonck 23 April 2014

There and back again A short trip to Fourier Space Janet Vonck 23 April 2014 Where can I find a Fourier Transform? Fourier Transforms are ubiquitous in structural biology: X-ray diffraction Spectroscopy