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Hello,<br>
<br>
<blockquote cite="mid:54807140.2030608@shelx.uni-ac.gwdg.de"
type="cite">
<pre wrap="">I guess you are
arguing that by using constraints there are more data available to
refine B-values AND occupancy. You are probably aware that these to
numbers are strongly correlated (>=90%!!) so that it is very tricky to
get get reliable numbers anyhow</pre>
</blockquote>
<br>
sometimes numbers excite me! So this one caught my attention and I
decided to entertain myself. <br>
<br>
First off, an obvious statement: occupancy defines peak's height and
B-factor defines its shape. Therefore one cannot be entirely
compensated with the other.<br>
<br>
Now let's see if and how occupancy and B-factor are correlated. For
this let's take an atom and plot its electron density distribution
with occupancy q=1 and some B value; let's call this density rho_ref
(reference map). Then let's vary occupancy from 0.1 to 1.0 (with
step 0.1) and for each trial occupancy value find such B_opt that
corresponding electron density distribution fits rho_ref as good as
possible; let's call it rho_opt (map corresponding to optimal
B_opt). In the end we will have ten occupancy values and ten
corresponding optimal B values so that we can calculate the
correlation between two sets of numbers (q, B_opt). In addition
let's calculate correlation and R-factor for rho_ref and rho_opt.<br>
<br>
We will repeat the numerical experiment defined above with:<br>
� a) different starting B values (10, 30, 50, 80), <br>
� b) different atoms H, C, S, <br>
� c) exact electron density distribution as well as its Fourier
image of 2A resolution.<br>
<br>
Attached script does it all in one go. Also it illustrates the
beauty of CCTBX that allows to do this so easily!<br>
<br>
Here are the numbers:<br>
<br>
<small><font face="Courier New, Courier, monospace">Resolution: None
(exact
map)----------------------------------------------------------<br>
� atom: H<br>
��� B: 10<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 1.00� 1.00� 2.00� 3.00� 5.00�
6.00� 7.00� 9.00 10.00<br>
����� CC(rho_ref,rho_opt):� 0.95� 0.95� 0.95� 0.97� 0.98� 0.99�
0.99� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 34.94 34.94 34.94 28.30 23.09 14.83
11.36� 8.19� 2.55� 0.00<br>
����� CC(q,B):�� 0.97<br>
��� B: 30<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 4.00� 7.00 11.00 14.00 17.00
21.00 24.00 27.00 30.00<br>
����� CC(rho_ref,rho_opt):� 0.85� 0.91� 0.95� 0.97� 0.98� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 54.39 42.43 34.42 26.09 20.84 16.16
10.59� 6.81� 3.29� 0.00<br>
����� CC(q,B):�� 1.00<br>
��� B: 50<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 3.00� 9.00 15.00 20.00 26.00 31.00
36.00 41.00 45.00 50.00<br>
����� CC(rho_ref,rho_opt):� 0.84� 0.91� 0.95� 0.97� 0.98� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 55.33 42.14 32.91 26.59 20.01 15.15
10.72� 6.64� 3.59� 0.00<br>
����� CC(q,B):�� 1.00<br>
��� B: 80<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 8.00 18.00 27.00 35.00 43.00 51.00
59.00 66.00 73.00 80.00<br>
����� CC(rho_ref,rho_opt):� 0.85� 0.92� 0.95� 0.97� 0.98� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 53.74 41.14 32.57 26.13 20.44 15.31
10.64� 6.86� 3.32� 0.00<br>
����� CC(q,B):�� 1.00<br>
� atom: C<br>
��� B: 10<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 2.00� 3.00� 4.00� 5.00� 6.00�
7.00� 8.00� 9.00 10.00<br>
����� CC(rho_ref,rho_opt):� 0.79� 0.88� 0.93� 0.96� 0.98� 0.99�
0.99� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 62.77 49.83 39.70 31.37 24.32 18.23
12.89� 8.14� 3.87� 0.00<br>
����� CC(q,B):�� 1.00<br>
��� B: 30<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 4.00� 7.00 10.00 13.00 16.00 19.00
21.00 24.00 27.00 30.00<br>
����� CC(rho_ref,rho_opt):� 0.83� 0.91� 0.95� 0.97� 0.98� 0.99�
0.99� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 56.51 43.81 34.49 27.06 20.84 15.45
12.21� 7.76� 3.72� 0.00<br>
����� CC(q,B):�� 1.00<br>
��� B: 50<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 6.00 12.00 17.00 22.00 27.00 32.00
36.00 41.00 46.00 50.00<br>
����� CC(rho_ref,rho_opt):� 0.82� 0.91� 0.95� 0.97� 0.98� 0.99�
0.99� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 57.64 42.58 33.79 26.68 20.63 15.32
11.47� 7.06� 3.02� 0.00<br>
����� CC(q,B):�� 1.00<br>
��� B: 80<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� : 11.00 20.00 28.00 36.00 44.00 52.00
59.00 66.00 73.00 80.00<br>
����� CC(rho_ref,rho_opt):� 0.84� 0.91� 0.95� 0.97� 0.98� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 54.69 41.90 33.51 26.57 20.56 15.22
10.98� 7.06� 3.41� 0.00<br>
����� CC(q,B):�� 1.00<br>
� atom: S<br>
��� B: 10<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 2.00� 3.00� 4.00� 5.00� 6.00�
7.00� 8.00� 9.00 10.00<br>
����� CC(rho_ref,rho_opt):� 0.82� 0.89� 0.93� 0.96� 0.98� 0.99�
0.99� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 59.32 47.29 38.28 30.75 24.21 18.39
13.15� 8.39� 4.03� 0.00<br>
����� CC(q,B):�� 1.00<br>
��� B: 30<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 4.00� 8.00 11.00 14.00 17.00 19.00
22.00 25.00 27.00 30.00<br>
����� CC(rho_ref,rho_opt):� 0.82� 0.91� 0.95� 0.97� 0.98� 0.99�
0.99� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 57.49 42.56 33.98 26.75 20.48 16.72
11.57� 6.91� 4.03� 0.00<br>
����� CC(q,B):�� 1.00<br>
��� B: 50<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 8.00 13.00 19.00 23.00 28.00 33.00
37.00 42.00 46.00 50.00<br>
����� CC(rho_ref,rho_opt):� 0.84� 0.91� 0.95� 0.97� 0.98� 0.99�
0.99� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 54.25 43.18 32.90 27.17 20.88 15.31
11.27� 6.64� 3.21� 0.00<br>
����� CC(q,B):�� 1.00<br>
��� B: 80<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� : 13.00 22.00 30.00 38.00 46.00 53.00
60.00 67.00 73.00 80.00<br>
����� CC(rho_ref,rho_opt):� 0.84� 0.91� 0.95� 0.97� 0.98� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 53.98 41.82 33.40 26.32 20.16 15.32
10.91� 6.83� 3.57� 0.00<br>
����� CC(q,B):�� 1.00<br>
Resolution: 2.0
----------------------------------------------------------------------<br>
� atom: H<br>
��� B: 10<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 1.00� 1.00� 1.00� 1.00� 1.00�
1.00� 2.00� 6.00 10.00<br>
����� CC(rho_ref,rho_opt):� 1.00� 1.00� 1.00� 1.00� 1.00� 1.00�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� :� 5.93� 5.93� 5.93� 5.93� 5.93� 5.93�
5.93� 5.28� 2.66� 0.00<br>
����� CC(q,B):�� 0.72<br>
��� B: 30<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 1.00� 1.00� 1.00� 4.00 10.00
16.00 21.00 26.00 30.00<br>
����� CC(rho_ref,rho_opt):� 0.99� 0.99� 0.99� 0.99� 0.99� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 18.17 18.17 18.17 18.17 16.35 12.62�
8.83� 5.66� 2.50� 0.00<br>
����� CC(q,B):�� 0.95<br>
��� B: 50<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 1.00� 2.00 12.00 20.00 27.00
33.00 39.00 45.00 50.00<br>
����� CC(rho_ref,rho_opt):� 0.97� 0.97� 0.97� 0.98� 0.99� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 27.44 27.44 26.91 21.35 16.76 12.70�
9.30� 5.94� 2.66� 0.00<br>
����� CC(q,B):�� 0.99<br>
��� B: 80<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 6.00 20.00 31.00 41.00 50.00
58.00 66.00 73.00 80.00<br>
����� CC(rho_ref,rho_opt):� 0.93� 0.94� 0.96� 0.98� 0.99� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 36.70 34.44 27.69 22.24 17.34 13.03�
9.33� 5.80� 2.84� 0.00<br>
����� CC(q,B):�� 1.00<br>
� atom: C<br>
��� B: 10<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 1.00� 1.00� 1.00� 1.00� 1.00�
1.00� 3.00� 6.00 10.00<br>
����� CC(rho_ref,rho_opt):� 1.00� 1.00� 1.00� 1.00� 1.00� 1.00�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� :� 5.96� 5.96� 5.96� 5.96� 5.96� 5.96�
5.96� 4.65� 2.67� 0.00<br>
����� CC(q,B):�� 0.75<br>
��� B: 30<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 1.00� 1.00� 1.00� 5.00 11.00
16.00 21.00 26.00 30.00<br>
����� CC(rho_ref,rho_opt):� 0.99� 0.99� 0.99� 0.99� 0.99� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 18.37 18.37 18.37 18.37 15.93 12.16�
8.96� 5.75� 2.54� 0.00<br>
����� CC(q,B):�� 0.95<br>
��� B: 50<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 1.00� 3.00 12.00 20.00 27.00
33.00 39.00 45.00 50.00<br>
����� CC(rho_ref,rho_opt):� 0.97� 0.97� 0.97� 0.98� 0.99� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 27.82 27.82 26.75 21.70 17.07 12.95�
9.48� 6.06� 2.71� 0.00<br>
����� CC(q,B):�� 0.99<br>
��� B: 80<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 7.00 21.00 32.00 41.00 50.00
58.00 66.00 73.00 80.00<br>
����� CC(rho_ref,rho_opt):� 0.93� 0.94� 0.96� 0.98� 0.99� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 37.14 34.45 27.63 22.10 17.64 13.25�
9.48� 5.90� 2.88� 0.00<br>
����� CC(q,B):�� 1.00<br>
� atom: S<br>
��� B: 10<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 1.00� 1.00� 1.00� 1.00� 1.00�
1.00� 3.00� 7.00 10.00<br>
����� CC(rho_ref,rho_opt):� 1.00� 1.00� 1.00� 1.00� 1.00� 1.00�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� :� 5.88� 5.88� 5.88� 5.88� 5.88� 5.88�
5.88� 4.60� 1.99� 0.00<br>
����� CC(q,B):�� 0.76<br>
��� B: 30<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 1.00� 1.00� 1.00� 6.00 11.00
17.00 21.00 26.00 30.00<br>
����� CC(rho_ref,rho_opt):� 0.99� 0.99� 0.99� 0.99� 0.99� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 18.46 18.46 18.46 18.46 15.43 12.30�
8.45� 5.84� 2.59� 0.00<br>
����� CC(q,B):�� 0.96<br>
��� B: 50<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 1.00� 4.00 13.00 21.00 28.00
34.00 40.00 45.00 50.00<br>
����� CC(rho_ref,rho_opt):� 0.97� 0.97� 0.97� 0.98� 0.99� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 28.30 28.30 26.67 21.63 16.92 12.75�
9.18� 5.68� 2.81� 0.00<br>
����� CC(q,B):�� 0.99<br>
��� B: 80<br>
����� trial q����������� :� 0.10� 0.20� 0.30� 0.40� 0.50� 0.60�
0.70� 0.80� 0.90� 1.00<br>
����� B_opt������������� :� 1.00� 9.00 22.00 33.00 43.00 51.00
59.00 66.00 73.00 80.00<br>
����� CC(rho_ref,rho_opt):� 0.93� 0.94� 0.96� 0.98� 0.99� 0.99�
1.00� 1.00� 1.00� 1.00<br>
����� R(%)�������������� : 37.91 34.26 27.88 22.25 17.20 13.22�
9.35� 6.10� 2.99� 0.00<br>
����� CC(q,B):�� 0.99<br>
</font></small><br>
What we see here is:<br>
� - correlation of q and B is indeed approaches 100%;<br>
� - map correlation is greater than 90% in most cases except a few
corner cases;<br>
� - the last column in all tests is an obvious sanity check (CC=1,
R=0 if exact B and q are used);<br>
� - R-factors are greater than zero except a trivial case. This is
the key that makes it possible to deconvolute q and B.<br>
<br>
All the best,<br>
Pavel<br>
<br>
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