Like so many rules of thumb, the 3-sigma fofc and 1-sigma 2fofc is a
reasonable guideline that works very well in most cases despite being
based on a flawed assumption. The "0.3% chance" of a peak being above 3
"sigmas" assumes that the histogram of electron density values is
Gaussian. It is not! In fact, it is a funny-looking bimodal
distribution (the peaks are protein and solvent regions). Programs like
SOLVE use this fact to identify the correct heavy-atom constellation
among all the wrong ones (which tend to produce maps with more
Gaussian-looking histograms).
It also seems to be a very common misconception that "1 sigma" is the
"noise level" in an electron density map. Not sure where that one got
started or how. No doubt due to the unfortunate use of the greek letter
"sigma" to denote a standard deviation in statistics. Indeed, the
"sigma" scaling of an electron density map is calculated the same way as
a standard deviation, but one need only calculate a "noise free" map
from a PDB file to notice that the "sigma" of such maps is not zero.
Does anyone know original references for sigma cutoff rules like this?
-James Holton
MAD Scientist
Ed Pozharski wrote:
I second Tim's opinion. In the days of CNS/O, there was a popular rule
to place waters in 3 sigma peaks that make chemical sense, then
re-refine and keep those waters that produce more than 1 sigma in 2fo-fc
map. (With Coot the default cutoff is 5).
There could be a bizarre probabilistic argument for a particular choice
of sigma cutoff - with 3 sigmas you have ~0.3% chance of a particular
peak to be simply a random spike. Which means that if the map is on,
say, 0.5A grid, there is a decent chance to have one such peak per
3.5x3.5x3.5A volume. With 5 sigmas the size of the cube goes up to
~60x60x60A, so 5 sigma peaks are almost guaranteed not to be flukes.
On Sat, 2010-04-17 at 22:46 +0200, Tim Gruene wrote:
Hello Sudhir Kumar,
most of all the waters in your structure should make chemical sense. When the
density around the water is weak it may just mean that the water is not fully
occupied.
Tim
On Sat, Apr 17, 2010 at 09:47:35PM +0900, Sudhir Kumar wrote:
hi all
sorry for such a basic query, i'ld like to know what is the acceptable sigma
cut off for waters to be kept in a model if data is of about 1.6 A.
thanks in advance
Sudhir Kumar
Research Scholar
Structural Biology Laboratory
SLS, JNU,
New Delhi-110067
