Good point; I've tested this (n=1) in the past with a high-resolution dataset (synchrotron data) and low-resolution dataset (in-house) of crystals of the same protein grown in the same drop. Same space group, same unit cell. B-factors for the low-resolution dataset were higher. After dividing every individual B-factor by the average B-factor of each, the normalized-B-factor-versus-residue plot was identical for both structures. Adding or subtracting a constant value didn't do that.
As I pointed out, this is only n=1, but comparing the high-and low-resolution structures of the same condition should give the answer as to which B-factor normalization is the most appropriate. Filip Van Petegem On Mon, Mar 4, 2013 at 11:16 AM, Jacob Keller < j-kell...@fsm.northwestern.edu> wrote: > You only entertain addition+subtraction--why not use > multiplication/division to normalize the b-factors? > > JPK > > > On Mon, Mar 4, 2013 at 2:04 PM, James Holton <jmhol...@lbl.gov> wrote: > >> Formally, the "best" way to compare B factors in two structures with >> different average B is to add a constant to all the B factors in the low-B >> structure until the average B factor is the same in both structures. Then >> you can compare "apples to apples" as it were. The "extra B" being added >> is equivalent to "blurring" the more well-ordered map to make it match the >> less-ordered one. Subtracting a B factor from the less-ordered structure is >> "sharpening", and the reason why you shouldn't do that here is because >> you'd be assuming that a sharpened map has just as much structural >> information as the better diffracting crystal, and that's obviously no true >> (not as many spots). In reality, your comparison will always be limited >> by the worst-resolution data you have. >> >> Another reason to add rather than subtract a B factor is because B >> factors are not really "linear" with anything sensible. Yes, B=50 is "more >> disordered" than B=25, but is it "twice as disordered"? That depends on >> what you mean by "disorder", but no matter how you look at it, the answer >> is generally "no". >> >> One way to define the "degree of disorder" is the volume swept out by the >> atom's nucleus as it "vibrates" (or otherwise varies from cell to cell). >> This is NOT proportional to the B-factor, but rather the 3/2 power of the >> B factor. Yes, 3/2 power. The value of "B", is proportional to the >> SQUARE of the width of the probability distribution of the nucleus, so to >> get the volume of space swept out by it you have to take the square root to >> get something proportional the the width and then you take the 3rd power to >> get something proportional to the volume. >> >> An then, of course, if you want to talk about the electron cloud (which >> is what x-rays "see") and not the nuclear position (which you can only see >> if you are a neutron person), then you have to "add" a B factor of about 8 >> to every atom to account for the intrinsic width of the electron cloud. >> Formally, the B factor is "convoluted" with the intrinsic atomic form >> factor, but a "native" B factor of 8 is pretty close for most atoms. >> >> For those of you who are interested in something more exact than >> "proportional" the equation for the nuclear probability distribution >> generated by a given B factor is: >> kernel_B(r) = (4*pi/B)^1.5*exp(-4*pi^2/B*r^**2) >> where "r" is the distance from the "average position" (aka the x-y-z >> coordinates in the PDB file). Note that the width of this distribution of >> atomic positions is not really an "error bar", it is a "range". There's a >> difference between an atom actually being located in a variety of places vs >> not knowing the centroid of all these locations. Remember, you're >> averaging over trillions of unit cells. If you collect a different dataset >> from a similar crystal and re-refine the structure the final x-y-z >> coordinate assigned to the atom will not change all that much. >> >> The full-width at half-maximum (FWHM) of this kernel_B distribution is: >> fwhm = 0.1325*sqrt(B) >> and the probability of finding the nucleus within this radius is actually >> only about 29%. The radius that contains the nucleus half the time is >> about 1.3 times wider, or: >> r_half = 0.1731*sqrt(B) >> >> That is, for B=25, the atomic nucleus is within 0.87 A of its average >> position 50% of the time (a volume of 2.7 A^3). Whereas for B=50, it is >> within 1.22 A 50% of the time (7.7 A^3). Note that although B=50 is twice >> as big as B=25, the half-occupancy radius 0.87 A is not half as big as 1.22 >> A, nor are the volumes 2.7 and 7.7 A^3 related by a factor of two. >> >> Why is this important for comparing two structures? Since the B factor >> is non-linear with disorder, it is important to have a common reference >> point when comparing them. If the low-B structure has two atoms with B=10 >> and B=15 with average overall B=12, that might seem to be "significant" >> (almost a factor of two in the half-occupancy volume) but if the other >> structure has an average B factor of 80, then suddenly 78 vs 83 doesn't >> seem all that different (only a 10% change). Basically, a difference that >> would be "significant" in a high-resolution structure is "washed out" by >> the overall crystallographic B factor of the low-resolution structure in >> this case. >> >> Whether or not a 10% difference is "significant" depends on how accurate >> you think your B factors are. If you "kick" your coordinates (aka using >> "noise" in PDBSET) and re-refine, how much do the final B factors change? >> >> -James Holton >> MAD Scientist >> >> >> On 2/25/2013 12:08 PM, Yarrow Madrona wrote: >> >>> Hello, >>> >>> Does anyone know a good method to compare B-factors between structures? I >>> would like to compare mutants to a wild-type structure. >>> >>> For example, structure2 has a higher B-factor for residue X but how can I >>> show that this is significant if the average B-factor is also higher? >>> Thank you for your help. >>> >>> >>> > > > -- > ******************************************* > Jacob Pearson Keller, PhD > Postdoctoral Associate > HHMI Janelia Farms Research Campus > email: j-kell...@northwestern.edu > ******************************************* > -- Filip Van Petegem, PhD Associate Professor The University of British Columbia Dept. of Biochemistry and Molecular Biology 2350 Health Sciences Mall - Rm 2.356 Vancouver, V6T 1Z3 phone: +1 604 827 4267 email: filip.vanpete...@gmail.com http://crg.ubc.ca/VanPetegem/
