we can use model B factors to validate structures - see Analysis and validation of macromolecular B values R. C. Masmaliyeva and G. N. Murshudov Acta Cryst. (2019). D75, 505-518 https://doi.org/10.1107/S2059798319004807
HTH Kay On Sun, 8 Mar 2020 09:08:32 +0000, Rangana Warshamanage <ranga...@gmail.com> wrote: >"The best estimate we have of the "true" B factor is the model B factors >we get at the end of refinement, once everything is converged, after we >have done all the building we can. It is this "true B factor" that is a >property of the data, not the model, " > >If this is the case, why can't we use model B factors to validate our >structure? I know some people are skeptical about this approach because B >factors are refinable parameters. > >Rangana > >On Sat, Mar 7, 2020 at 8:01 PM James Holton <jmhol...@lbl.gov> wrote: > >> Yes, that's right. Model B factors are fit to the data. That Boverall >> gets added to all atomic B factors in the model before the structure is >> written out, yes? >> >> The best estimate we have of the "true" B factor is the model B factors >> we get at the end of refinement, once everything is converged, after we >> have done all the building we can. It is this "true B factor" that is a >> property of the data, not the model, and it has the relationship to >> resolution and map appearance that I describe below. Does that make sense? >> >> -James Holton >> MAD Scientist >> >> On 3/7/2020 10:45 AM, dusan turk wrote: >> > James, >> > >> > The case you’ve chosen is not a good illustration of the relationship >> between atomic B and resolution. The problem is that during scaling of >> Fcalc to Fobs also B-factor difference between the two sets of numbers is >> minimized. In the simplest form with two constants Koverall and Boverall >> it looks like this: >> > >> > sum_to_be_minimized = sum (FOBS**2 - Koverall * FCALC**2 * exp(-1/d**2 >> * Boverall) ) >> > >> > Then one can include bulk solvent correction, anisotripic scaling, … In >> PHENIX it gets quite complex. >> > >> > Hence, almost regardless of the average model B you will always get the >> same map, because the “B" of the map will reflect the B of the FOBS. When >> all atomic Bs are equal then they are also equal to average B. >> > >> > best, dusan >> > >> > >> >> On 7 Mar 2020, at 01:01, CCP4BB automatic digest system < >> lists...@jiscmail.ac.uk> wrote: >> >> >> >>> On Thu, 5 Mar 2020 01:11:33 +0100, James Holton <jmhol...@lbl.gov> >> wrote: >> >>> >> >>>> The funny thing is, although we generally regard resolution as a >> primary >> >>>> indicator of data quality the appearance of a density map at the >> classic >> >>>> "1-sigma" contour has very little to do with resolution, and >> everything >> >>>> to do with the B factor. >> >>>> >> >>>> Seriously, try it. Take any structure you like, set all the B factors >> to >> >>>> 30 with PDBSET, calculate a map with SFALL or phenix.fmodel and have a >> >>>> look at the density of tyrosine (Tyr) side chains. Even if you >> >>>> calculate structure factors all the way out to 1.0 A the holes in the >> >>>> Tyr rings look exactly the same: just barely starting to form. This >> is >> >>>> because the structure factors from atoms with B=30 are essentially >> zero >> >>>> out at 1.0 A, and adding zeroes does not change the map. You can >> adjust >> >>>> the contour level, of course, and solvent content will have some >> effect >> >>>> on where the "1-sigma" contour lies, but generally B=30 is the point >> >>>> where Tyr side chains start to form their holes. Traditionally, this >> is >> >>>> attributed to 1.8A resolution, but it is really at B=30. The point >> >>>> where waters first start to poke out above the 1-sigma contour is at >> >>>> B=60, despite being generally attributed to d=2.7A. >> >>>> >> >>>> Now, of course, if you cut off this B=30 data at 3.5A then the Tyr >> side >> >>>> chains become blobs, but that is equivalent to collecting data with >> the >> >>>> detector way too far away and losing your high-resolution spots off >> the >> >>>> edges. I have seen a few people do that, but not usually for a >> >>>> published structure. Most people fight very hard for those faint, >> >>>> barely-existing high-angle spots. But why do we do that if the map is >> >>>> going to look the same anyway? The reason is because resolution and B >> >>>> factors are linked. >> >>>> >> >>>> Resolution is about separation vs width, and the width of the density >> >>>> peak from any atom is set by its B factor. Yes, atoms have an >> intrinsic >> >>>> width, but it is very quickly washed out by even modest B factors (B > >> >>>> 10). This is true for both x-ray and electron form factors. To a very >> >>>> good approximation, the FWHM of C, N and O atoms is given by: >> >>>> FWHM= sqrt(B*log(2))/pi+0.15 >> >>>> >> >>>> where "B" is the B factor assigned to the atom and the 0.15 fudge >> factor >> >>>> accounts for its intrinsic width when B=0. Now that we know the peak >> >>>> width, we can start to ask if two peaks are "resolved". >> >>>> >> >>>> Start with the classical definition of "resolution" (call it after >> Airy, >> >>>> Raleigh, Dawes, or whatever famous person you like), but essentially >> you >> >>>> are asking the question: "how close can two peaks be before they merge >> >>>> into one peak?". For Gaussian peaks this is 0.849*FWHM. Simple >> enough. >> >>>> However, when you look at the density of two atoms this far apart you >> >>>> will see the peak is highly oblong. Yes, the density has one maximum, >> >>>> but there are clearly two atoms in there. It is also pretty obvious >> the >> >>>> long axis of the peak is the line between the two atoms, and if you >> fit >> >>>> two round atoms into this peak you recover the distance between them >> >>>> quite accurately. Are they really not "resolved" if it is so clear >> >>>> where they are? >> >>>> >> >>>> In such cases you usually want to sharpen, as that will make the >> oblong >> >>>> blob turn into two resolved peaks. Sharpening reduces the B factor >> and >> >>>> therefore FWHM of every atom, making the "resolution" (0.849*FWHM) a >> >>>> shorter distance. So, we have improved resolution with sharpening! >> Why >> >>>> don't we always do this? Well, the reason is because of noise. >> >>>> Sharpening up-weights the noise of high-order Fourier terms and >> >>>> therefore degrades the overall signal-to-noise (SNR) of the map. This >> >>>> is what I believe Colin would call reduced "contrast". Of course, >> since >> >>>> we view maps with a threshold (aka contour) a map with SNR=5 will look >> >>>> almost identical to a map with SNR=500. The "noise floor" is generally >> >>>> well below the 1-sigma threshold, or even the 0-sigma threshold >> >>>> (https://doi.org/10.1073/pnas.1302823110). As you turn up the >> >>>> sharpening you will see blobs split apart and also see new peaks >> rising >> >>>> above your map contouring threshold. Are these new peaks real? Or >> are >> >>>> they noise? That is the difference between SNR=500 and SNR=5, >> >>>> respectively. The tricky part of sharpening is knowing when you have >> >>>> reached the point where you are introducing more noise than signal. >> >>>> There are some good methods out there, but none of them are perfect. >> >>>> >> >>>> What about filtering out the noise? An ideal noise suppression filter >> >>>> has the same shape as the signal (I found that in Numerical Recipes), >> >>>> and the shape of the signal from a macromolecule is a Gaussian in >> >>>> reciprocal space (aka straight line on a Wilson plot). This is true, >> by >> >>>> the way, for both a molecule packed into a crystal or free in >> solution. >> >>>> So, the ideal noise-suppression filter is simply applying a B factor. >> >>>> Only problem is: sharpening is generally done by applying a negative B >> >>>> factor, so applying a Gaussian blur is equivalent to just not >> sharpening >> >>>> as much. So, we are back to "optimal sharpening" again. >> >>>> >> >>>> Why not use a filter that is non-Gaussian? We do this all the time! >> >>>> Cutting off the data at a given resolution (d) is equivalent to >> blurring >> >>>> the map with this function: >> >>>> >> >>>> kernel_d(r) = 4/3*pi/d**3*sinc3(2*pi*r/d) >> >>>> sinc3(x) = (x==0?1:3*(sin(x)/x-cos(x))/(x*x)) >> >>>> >> >>>> where kernel_d(r) is the normalized weight given to a point "r" >> Angstrom >> >>>> away from the center of each blurring operation, and "sinc3" is the >> >>>> Fourier synthesis of a solid sphere. That is, if you make an HKL file >> >>>> with all F=1 and PHI=0 out to a resolution d, then effectively all >> hkls >> >>>> beyond the resolution limit are zero. If you calculate a map with >> those >> >>>> Fs, you will find the kernel_d(r) function at the origin. What that >> >>>> means is: by applying a resolution cutoff, you are effectively >> >>>> multiplying your data by this sphere of unit Fs, and since a >> >>>> multiplication in reciprocal space is a convolution in real space, the >> >>>> effect is convoluting (blurring) with kernel_d(x). >> >>>> >> >>>> For comparison, if you apply a B factor, the real-space blurring >> kernel >> >>>> is this: >> >>>> kernel_B(r) = (4*pi/B)**1.5*exp(-4*pi**2/B*r*r) >> >>>> >> >>>> If you graph these two kernels (format is for gnuplot) you will find >> >>>> that they have the same FWHM whenever B=80*(d/3)**2. This "rule" is >> the >> >>>> one I used for my resolution demonstration movie I made back in the >> late >> >>>> 20th century: >> >>>> https://bl831.als.lbl.gov/~jamesh/movies/index.html#resolution >> >>>> >> >>>> What I did then was set all atomic B factors to B = 80*(d/3)^2 and >> then >> >>>> cut the resolution at "d". Seemed sensible at the time. I suppose I >> >>>> could have used the PDB-wide average atomic B factor reported for >> >>>> structures with resolution "d", which roughly follows: >> >>>> B = 4*d**2+12 >> >>>> https://bl831.als.lbl.gov/~jamesh/pickup/reso_vs_avgB.png >> >>>> >> >>>> The reason I didn't use this formula for the movie is because I didn't >> >>>> figure it out until about 10 years later. These two curves cross at >> >>>> 1.5A, but diverge significantly at poor resolution. So, which one is >> >>>> right? It depends on how well you can measure really really faint >> >>>> spots, and we've been getting better at that in recent decades. >> >>>> >> >>>> So, what I'm trying to say here is that just because your data has >> CC1/2 >> >>>> or FSC dropping off to insignificance at 1.8 A doesn't mean you are >> >>>> going to see holes in Tyr side chains. However, if you measure your >> >>>> weak, high-res data really well (high multiplicity), you might be able >> >>>> to sharpen your way to a much clearer map. >> >>>> >> >>>> -James Holton >> >>>> MAD Scientist >> >>>> >> > ######################################################################## >> > >> > To unsubscribe from the CCP4BB list, click the following link: >> > https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1 >> >> ######################################################################## >> >> To unsubscribe from the CCP4BB list, click the following link: >> https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1 >> > >######################################################################## > >To unsubscribe from the CCP4BB list, click the following link: >https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1 > ######################################################################## To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1
