# [phenixbb] neutron scattering table for specific metal isotope

Dale Tronrud detBB at daletronrud.com
Thu Dec 4 15:16:00 PST 2014

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You haven't quite finished the job Pavel.  In your test you are
always starting with an atom with occupancy of 1.  Those atoms we
usually know have an occupancy of 1 so we constrain to that value.
The real question come up with the occupancy is less than one, but we
don't know either the B or the Occ.

Then you need to plot R value in 2-D as both Occ and B are varied.
The correlation we all talk of is due to a diagonal line of minimal R
in that plot.  Since there are a bunch of different combinations of B
and Occ that give similar fit we end up with a relationship between
the possible values.  Certainly when you change EITHER Occ or B alone
(as you have done here) you see a change to the fit to the data.

Use your CCTBX wizardry to show us the 2-D plot!

Dale Tronrud

On 12/4/2014 2:29 PM, Pavel Afonine wrote:
> Hello,
>
>> 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
>
> sometimes numbers excite me! So this one caught my attention and I
> decided to entertain myself.
>
> 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.
>
> 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.
>
> We will repeat the numerical experiment defined above with: a)
> different starting B values (10, 30, 50, 80), b) different atoms H,
> C, S, c) exact electron density distribution as well as its Fourier
> image of 2A resolution.
>
> Attached script does it all in one go. Also it illustrates the
> beauty of CCTBX that allows to do this so easily!
>
> Here are the numbers:
>
> Resolution: None (exact
> map)----------------------------------------------------------
> atom: H B: 10 trial q            :  0.10  0.20  0.30  0.40  0.50
> 0.60  0.70 0.80  0.90  1.00 B_opt              :  1.00  1.00  1.00
> 2.00  3.00  5.00  6.00 7.00  9.00 10.00 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 R(%)
> : 34.94 34.94 34.94 28.30 23.09 14.83 11.36 8.19  2.55  0.00
> CC(q,B):   0.97 B: 30 trial q            :  0.10  0.20  0.30  0.40
> 0.50  0.60  0.70 0.80  0.90  1.00 B_opt              :  1.00  4.00
> 7.00 11.00 14.00 17.00 21.00 24.00 27.00 30.00 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 R(%)
> : 54.39 42.43 34.42 26.09 20.84 16.16 10.59 6.81  3.29  0.00
> CC(q,B):   1.00 B: 50 trial q            :  0.10  0.20  0.30  0.40
> 0.50  0.60  0.70 0.80  0.90  1.00 B_opt              :  3.00  9.00
> 15.00 20.00 26.00 31.00 36.00 41.00 45.00 50.00
> 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 R(%)               : 55.33 42.14 32.91 26.59 20.01 15.15
> 10.72 6.64  3.59  0.00 CC(q,B):   1.00 B: 80 trial q            :
> 0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  8.00 18.00 27.00 35.00 43.00 51.00 59.00 66.00 73.00 80.00
> 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 R(%)               : 53.74 41.14 32.57 26.13 20.44 15.31
> 10.64 6.86  3.32  0.00 CC(q,B):   1.00 atom: C B: 10 trial q
> :  0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  1.00  2.00  3.00  4.00  5.00  6.00  7.00 8.00  9.00 10.00
> 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 R(%)               : 62.77 49.83 39.70 31.37 24.32 18.23
> 12.89 8.14  3.87  0.00 CC(q,B):   1.00 B: 30 trial q            :
> 0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  4.00  7.00 10.00 13.00 16.00 19.00 21.00 24.00 27.00 30.00
> 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 R(%)               : 56.51 43.81 34.49 27.06 20.84 15.45
> 12.21 7.76  3.72  0.00 CC(q,B):   1.00 B: 50 trial q            :
> 0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  6.00 12.00 17.00 22.00 27.00 32.00 36.00 41.00 46.00 50.00
> 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 R(%)               : 57.64 42.58 33.79 26.68 20.63 15.32
> 11.47 7.06  3.02  0.00 CC(q,B):   1.00 B: 80 trial q            :
> 0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> : 11.00 20.00 28.00 36.00 44.00 52.00 59.00 66.00 73.00 80.00
> 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 R(%)               : 54.69 41.90 33.51 26.57 20.56 15.22
> 10.98 7.06  3.41  0.00 CC(q,B):   1.00 atom: S B: 10 trial q
> :  0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  1.00  2.00  3.00  4.00  5.00  6.00  7.00 8.00  9.00 10.00
> 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 R(%)               : 59.32 47.29 38.28 30.75 24.21 18.39
> 13.15 8.39  4.03  0.00 CC(q,B):   1.00 B: 30 trial q            :
> 0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  4.00  8.00 11.00 14.00 17.00 19.00 22.00 25.00 27.00 30.00
> 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 R(%)               : 57.49 42.56 33.98 26.75 20.48 16.72
> 11.57 6.91  4.03  0.00 CC(q,B):   1.00 B: 50 trial q            :
> 0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  8.00 13.00 19.00 23.00 28.00 33.00 37.00 42.00 46.00 50.00
> 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 R(%)               : 54.25 43.18 32.90 27.17 20.88 15.31
> 11.27 6.64  3.21  0.00 CC(q,B):   1.00 B: 80 trial q            :
> 0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> : 13.00 22.00 30.00 38.00 46.00 53.00 60.00 67.00 73.00 80.00
> 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 R(%)               : 53.98 41.82 33.40 26.32 20.16 15.32
> 10.91 6.83  3.57  0.00 CC(q,B):   1.00 Resolution: 2.0
> ----------------------------------------------------------------------
>
>
atom: H
> B: 10 trial q            :  0.10  0.20  0.30  0.40  0.50  0.60
> 0.70 0.80  0.90  1.00 B_opt              :  1.00  1.00  1.00  1.00
> 1.00  1.00  1.00 2.00  6.00 10.00 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 R(%)               :
> 5.93  5.93  5.93  5.93  5.93  5.93  5.93 5.28  2.66  0.00 CC(q,B):
> 0.72 B: 30 trial q            :  0.10  0.20  0.30  0.40  0.50  0.60
> 0.70 0.80  0.90  1.00 B_opt              :  1.00  1.00  1.00  1.00
> 4.00 10.00 16.00 21.00 26.00 30.00 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 R(%)               :
> 18.17 18.17 18.17 18.17 16.35 12.62  8.83 5.66  2.50  0.00 CC(q,B):
> 0.95 B: 50 trial q            :  0.10  0.20  0.30  0.40  0.50  0.60
> 0.70 0.80  0.90  1.00 B_opt              :  1.00  1.00  2.00 12.00
> 20.00 27.00 33.00 39.00 45.00 50.00 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 R(%)
> : 27.44 27.44 26.91 21.35 16.76 12.70  9.30 5.94  2.66  0.00
> CC(q,B):   0.99 B: 80 trial q            :  0.10  0.20  0.30  0.40
> 0.50  0.60  0.70 0.80  0.90  1.00 B_opt              :  1.00  6.00
> 20.00 31.00 41.00 50.00 58.00 66.00 73.00 80.00
> 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 R(%)               : 36.70 34.44 27.69 22.24 17.34 13.03
> 9.33 5.80  2.84  0.00 CC(q,B):   1.00 atom: C B: 10 trial q
> :  0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  1.00  1.00  1.00  1.00  1.00  1.00  1.00 3.00  6.00 10.00
> 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 R(%)               :  5.96  5.96  5.96  5.96  5.96  5.96
> 5.96 4.65  2.67  0.00 CC(q,B):   0.75 B: 30 trial q            :
> 0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  1.00  1.00  1.00  1.00  5.00 11.00 16.00 21.00 26.00 30.00
> 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 R(%)               : 18.37 18.37 18.37 18.37 15.93 12.16
> 8.96 5.75  2.54  0.00 CC(q,B):   0.95 B: 50 trial q            :
> 0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  1.00  1.00  3.00 12.00 20.00 27.00 33.00 39.00 45.00 50.00
> 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 R(%)               : 27.82 27.82 26.75 21.70 17.07 12.95
> 9.48 6.06  2.71  0.00 CC(q,B):   0.99 B: 80 trial q            :
> 0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  1.00  7.00 21.00 32.00 41.00 50.00 58.00 66.00 73.00 80.00
> 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 R(%)               : 37.14 34.45 27.63 22.10 17.64 13.25
> 9.48 5.90  2.88  0.00 CC(q,B):   1.00 atom: S B: 10 trial q
> :  0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  1.00  1.00  1.00  1.00  1.00  1.00  1.00 3.00  7.00 10.00
> 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 R(%)               :  5.88  5.88  5.88  5.88  5.88  5.88
> 5.88 4.60  1.99  0.00 CC(q,B):   0.76 B: 30 trial q            :
> 0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  1.00  1.00  1.00  1.00  6.00 11.00 17.00 21.00 26.00 30.00
> 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 R(%)               : 18.46 18.46 18.46 18.46 15.43 12.30
> 8.45 5.84  2.59  0.00 CC(q,B):   0.96 B: 50 trial q            :
> 0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  1.00  1.00  4.00 13.00 21.00 28.00 34.00 40.00 45.00 50.00
> 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 R(%)               : 28.30 28.30 26.67 21.63 16.92 12.75
> 9.18 5.68  2.81  0.00 CC(q,B):   0.99 B: 80 trial q            :
> 0.10  0.20  0.30  0.40  0.50  0.60  0.70 0.80  0.90  1.00 B_opt
> :  1.00  9.00 22.00 33.00 43.00 51.00 59.00 66.00 73.00 80.00
> 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 R(%)               : 37.91 34.26 27.88 22.25 17.20 13.22
> 9.35 6.10  2.99  0.00 CC(q,B):   0.99
>
> What we see here is: - correlation of q and B is indeed approaches
> 100%; - map correlation is greater than 90% in most cases except a
> few corner cases; - the last column in all tests is an obvious
> sanity check (CC=1, R=0 if exact B and q are used); - R-factors are
> greater than zero except a trivial case. This is the key that makes
> it possible to deconvolute q and B.
>
> All the best, Pavel
>
>
>
> _______________________________________________ phenixbb mailing
> list phenixbb at phenix-online.org
> http://phenix-online.org/mailman/listinfo/phenixbb
>
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