P212121

I was searching through the PDB last night and was amazed at the range of B-factors there were at a 3 Å resolution.

I then wondered, at what point should we not model the location of an atom?

First, a reminder:

The B-factor is a measure of the effective diameter of an atom’s electron density. Static (think crystal packing) and thermal motion can effectively disperse the electron density of a given atom, causing an increase in it’s B-factor. The B-factor is related to the rms error in an atom’s position (u) by the equation: B=79*u². For this reason, B-factors are related to resolution (reference).

Similar definitions of the B-factor can be found here and here.

If you end up searching through the PDB, you will find 1036 proteins (this number will change over time) deposited that have a 3.0 Å resolution.

First example:
PDB entry 2D7H, with the space group H32 and a unit cell, is as follows:
Length [Å] a 111.15 b 111.15 c 260.48
Angles [°] alpha 90.00 beta 90.00 gamma 120.00

Low B-factor
ATOM 759 CB ALA A 99 77.336 -1.412 30.730 1.00 21.08 C

High B-factor
ATOM 975 N MET B 24 38.372 12.422 49.773 1.00200.00 N
ATOM 976 CA MET B 24 39.225 11.256 49.976 1.00200.00 C
ATOM 977 C MET B 24 40.626 11.792 50.257 1.00200.00 C
ATOM 978 O MET B 24 41.131 12.633 49.511 1.00200.00 O
ATOM 1068 CB PHE B 36 45.647 -1.156 36.281 1.00200.00 C
ATOM 1069 CG PHE B 36 47.091 -1.333 35.905 1.00200.00 C
ATOM 1070 CD1 PHE B 36 48.100 -0.752 36.669 1.00200.00 C
ATOM 1071 CD2 PHE B 36 47.445 -2.085 34.788 1.00200.00 C
ATOM 1072 CE1 PHE B 36 49.442 -0.919 36.327 1.00200.00 C
ATOM 1073 CE2 PHE B 36 48.783 -2.257 34.436 1.00200.00 C
ATOM 1074 CZ PHE B 36 49.782 -1.673 35.209 1.00200.00 C
ATOM 1178 N GLU B 54 51.227 15.579 34.700 1.00200.00 N
ATOM 1179 CA GLU B 54 51.753 15.584 33.337 1.00200.00 C
ATOM 1180 C GLU B 54 50.633 15.768 32.310 1.00200.00 C
ATOM 1181 O GLU B 54 50.707 16.659 31.463 1.00200.00 O
ATOM 1187 N LEU B 55 49.599 14.932 32.381 1.00200.00 N
ATOM 1188 CA LEU B 55 48.477 15.043 31.448 1.00200.00 C
ATOM 1189 C LEU B 55 47.326 15.859 32.072 1.00200.00 C
ATOM 1190 O LEU B 55 47.344 16.161 33.269 1.00200.00 O
(I suspect that 200 is the maximum value allowed during data processing)

Second example:
PDB entry 3CSM in the same space group with a larger unit cell:
Length [Å] a 203.50 b 203.50 c 128.70
Angles [°] alpha 90.00 beta 90.00 gamma 120.00

Low B-factor
HETATM 4160 CH2 TRP A 300 60.946 11.402 30.293 1.00 2.00 C

High B-factor
HETATM 4192 O4 TSA A 400 35.340 17.976 38.640 1.00 96.69 O
(this is the last residue in the peptide, so it will often have a higher B-factor)

A number of other variables could effect the B-factor such as crystal packing, radiation damage or the use of partial occupancy. I find the difference between these two structures fascinating. Taking the B-factor into consideration is important, especially if a cartoon is presented without any crystallographic information.

Though not perfectly accurate, this scattering factor calculator can be used to examine the mean atom displacement for a carbon with a B-factor of 200.

The result is a 1.59 Å mean atom displacement which, as I mentioned in the introduction, makes one wonder at what point should we not model the location of an atom?