SHANUM interpretation

[Albert]

Hello,

I have some problems with trying to understand how SHANUM works. As an example, I ran SHANUM for the Importin alpha/beta complex (SASBDB id: SASDAC5) with Dmax = 11 nm. The results for this example can be found in the Konarev and Svergun paper (http://journals.iucr.org/m/issues/2015/ ... index.html).

If I run SHANUM ($ shanum -d SASDAC5.dat 19) I obtain:

Datafile=SASDAC5.dat
Dmax= 19.000000000000000
Smax= 6.2370099999999997
Nsh= 37.720736921316117
Nopt= 8
Sopt= 1.3227758541430708

Chi² vs Shannon channels

Chi_Rfac_vs_Nshannon.png (8.52 KiB) Viewed 1094 times

What's that?

DPR_vs_Nshannon.png (5.83 KiB) Viewed 1094 times

f function vs Shannon channels

Fun_M.png (6.72 KiB) Viewed 1094 times

Mi questions:

i) why the Nopt value suggested by shanum is 8 in spite of the minimum value in the f(M) function is at M = 11? (I have the same problems when I work with other noisy data)
ii) is the SASDAC5 data the same data used in the Konarev & Svergun paper? How can I reproduce the f(M) function in Fig 4a (Konarev & Svergun, 2015)?
iii) the DPR_vs_Nshannon.dat file has three columns, what does they mean? (dp/dr, (dp/dr)², alpha*Omega(pM) ...?)

Thanks!
A.

[konarev]

Hi Albert,

thank you for your inquiry, below you can find the answers.

>>i) why the Nopt value suggested by shanum is 8 in spite of the minimum value in the f(M) function is at M = 11? (I have the same problems >>when I work with other noisy data)

It is correct to check the minimum value of f(M), in majority of cases it gives a good estimate for the useful angular range.
However, in some cases (especially for noisy data) f(M) has a wide minimum plateau and the angular range, where a significant improvement of the fit quality of Shannon approximation happens, actually corresponds to lower M values.
That is why in the current implementation of Shanum, if f(M) function has a wide plateau, Nopt value is estimated in a more 'conservative' way selecting the M value after which no significant improvement of Chi^2 (or correlation map value) occurs.
It is also a good practice to compare the results for the data with and without error estimates, e.g. for this particular case
the correlation test will yield M=7 (that corresponds to the angular range up to 1.3 nm^-1
taken into account that the data becomes noisy already at 1.0 nm^-1)

>>ii) is the SASDAC5 data the same data used in the Konarev & Svergun paper? How can I reproduce the f(M) function in Fig 4a (Konarev & >>Svergun, 2015)?

It can be reproduced using the automated search for Dmax (that yields 17.2 nm), in this case f(M) will have minimum at M=8.

>>iii) the DPR_vs_Nshannon.dat file has three columns, what does they mean? (dp/dr, (dp/dr)², alpha*Omega(pM) ...?)

The first column - the number of Shannon channels used for the data approximation,
the second column - is Omega(pM) (the integral first derivative of p(r))
the third column - is the integral second derivative of p(r), calculated in a similar way as Omega(pM)
(the latter column does not influence any estimations of Shanum, it is stored just for information)

[Albert]

Thanks for your reply!

Please, let me raise another question.

I have obtained the following Shannon results in several times:

konarev.png (146.53 KiB) Viewed 1078 times

konarev2.png (97.92 KiB) Viewed 1078 times

According to the Chi²(M), Omega(pM) and f(M) functions the optimal number of Shannon channels is around 12. However, if I plot the fits as a function of M on the experimental data (without errors) I see that the best fitting is for the 5 Shannon channel (which corresponds to Smax = 2.4). This is in concordance with the fact that I can't obtain good p(r) functions with GNOM beyond S = 2.9.

How can I explain it?

Thanks!

[konarev]

It is difficult to clearly see the low angle part of the data, but still one can distinguish that Fit_Shannon_7.dat does not fit this part,
and with high probability Fit_Shannon5 and Fit_Shannon6 should also have systematic deviations from the data in this region.
Besides, Chi_Rfac_vs_Nshannon.dat points that the best fit quality corresponds to M=10-12.

It looks that the buffer was undersubtraced (or there is some sample/buffer mismatch), one can try to force
Porod asymptotics at higher angles by subtracting a constant from the data, it may improve p(r) fitting at higher angles.

[Albert]

Hello konarev,

This discussion is very useful for me, thanks a lot!

Is it acceptable a nice fitting with a slightly oscillating pair distribution function?

Dmax= 11.000000000000000
Smax= 6.0127709999999999
Nsh= 21.053168979251168
Nopt= 21

ACT.jpg (205.18 KiB) Viewed 1055 times

Thanks,
A.

[konarev]

It looks reasonable taking into account that Omega(M) function for M between 10 and 23 has similar values.

[Albert]

Thanks!