A B factor is the result of a curve fit. It is a big, complicated 3D
curve fit with internal couplings between parameters, but at the end of
the day macromolecular model refinement is still a "curve fit". It is
instructive to think of a linear slice through the map, because that way
you have a single "x" axis (position) and a single "y" axis (electron
density). What you get from this is a series of points (map grid
points) that you expect to form a peak at the position of an atom. The
B factor comes from the width of the best-fit curve to this peak. The
wider the peak, the bigger the B factor. Since every atom has only so
many electrons in it the height of the peak and the width are coupled.
Wider peaks are shorter and taller peaks are narrower.
As one might expect, if you try to fit a peak to something that is
basically flat, then you tend to get a very wide peak (high B factor).
It is also possible for the curve fit to "lock on" to a single blip of
noise, and this will give you a very sharp and narrow (but wrong) peak.
Modern refinement programs try to keep things like this from happening,
but the overall trend is that high B factors tend to arise from atom
built into featureless regions of your map.
So, yes, it is not incorrect to say that the B factors are determined by
the "quality" of the map, but you can also get high B factors using a
perfect map if you put the atoms in the wrong place. It is also
unfortunately a fallacy to think that getting "better phases" will make
your B factors get smaller. That doesn't happen. It is easy to
understand why if you think about it in "reciprocal space", where the B
factor describes how fast the intensities fall off with resolution.
Doesn't matter what the phases are. Yes, there are ways for high and
low B factors to cancel each other (and this is a common origin of what
is sometimes called "phase bias"), but on average the B factors describe
how amplitudes fall off. Think of it as working with data that has gone
through a smoothing filter. If the smoothing window is 3 A wide (~3A
resolution) then you don't expect to see any peaks with a
full-width-at-half-maximum (FWHM) narrower than that. For carbon, a
peak with FWHM = 3 A has a B factor of 114.
In actual fact, refinement is not generally done in real space as I
describe above, but rather in reciprocal space. This is because the
phases are not usually known and its more appropriate to fit directly to
the observed amplitudes without phases. However, real space and
reciprocal space are just two ways of representing the same thing: they
are directly related by a thing called the Fourier transform. You
neither gain nor loose information in a Fourier transform, you just
switch between representations for the same data.
HTH
-James Holton
MAD Scientist
On 5/23/2015 10:49 PM, Smith Liu wrote:
Dear All,
In the PDB file, the b-factors were only determined by the quality of
the map, is this view right or not?
Smith
