# [Chimera-users] Surprising "measure symmetry" result

Tom Goddard goddard at sonic.net
Fri Apr 4 11:13:03 PDT 2014

Hi Ingvar,

The basic trouble is that this map is so close to being cylindrically symmetric, ie identical at any rotation angle about z, that the “measure symmetry” command makes the wrong choice.  I put a print statement in the measure symmetry code and here are the correlation values it found for the map with a rotated copy of itself for cyclic n-fold symmetry with n = 2, 3, …, 24:

> measure sym #0 nmax 24
Symmetry emd_2463.map: C13, center 64 64 37
2 0.999913062795
3 0.999864979563
4 0.999949744672
5 0.991690288767
6 0.999886369722
7 0.994690864511
8 0.991400840587
9 0.992535268321
10 0.995822490928
11 0.999002374601
12 0.999904810469
13 0.999346674071
14 0.998135913568
15 0.996806980709
16 0.99559228476
17 0.994463541105
18 0.993546515874
19 0.992755122912
20 0.992182861668
21 0.99181103327
22 0.991574006772
23 0.991460398423
24 0.991401690757

Now the default correlation threshold for “measure symmetry” to recognize a symmetry is 0.99.  So the above table shows that with that criteria this map could be cyclic n-fold symmetric for any n = 2, …, 24.

So you might say let’s take the highest correlation value.  Looking at the table that is for n = 4, 4-fold symmetry.  The measure symmetry command doesn’t choose that wrong answer.  The map is C4 symmetric.  But a C12 map is automatically C6, C4, C3 and C2 symmetric since 6, 4, 3, and 2 divides evenly into 12.  So the measure symmetry command eliminates the choices for n that are divisors of another choice of n that has correlation > 0.99.  This is where C12 gets eliminated.  Because you see C24 has correlation of 0.991 and so C12 is eliminated because measure symmetry prefers to say the maps is C24.  Once you eliminate lower order symmetries the choices left are C13 through C24 and C13 has the highest correlation of those choices!

There are various ways you can get the right answer C12.  Using "measure sym  #0 nmax 23” to exclude 24-fold symmetry which is causing C12 to be knocked out the competition works.  Or setting a higher correlation threshold works since again C24 then gets eliminated because it doesn’t meet the correlation threshold.  Or changing the contour levels changes all the correlation values since it only considers grid points within the contour level when computing correlation.

The fundamental difficulty is that every choice of n for n-fold symmetry gives a correlation value greater than 0.99.  Maybe smarter code would not use a fixed cutoff value.  Instead it would look at the correlation values it finds, and choose a cutoff based on those.  But there is no easy answer.  If you look at the table of numbers above C4 symmetry has correlation 0.99994 while C12 has only 0.99990.  Why don’t I say the map has C4 symmetry and just happens to be very close to cylindrical so C12 is also high?  I guess you could look at the variance of the correlation values.  I see C8 is only 0.991, so clearly the map isn’t cylindrically symmetric at the 0.9999 level.  So some vary nuanced code could probably get the right answer.

I have no sound suggestion as to how to get the right answer consistently.  These EM maps were computed with an imposed symmetry, and the fundamental problem is that EMDB didn’t collect that information from the person who deposited the map.  And now it is very tricky to deduce what the symmetry the author used was in an automated way.  The solution is to collect this information from the author when they deposit the map — as this is very important information about the map.

Tom

On Apr 4, 2014, at 2:53 AM, ingvar <ingvar at ebi.ac.uk> wrote:

> Hello,
>
> I fetched entry EMD-2463 from EMDB and issued:
> measure symmetry #0 nMax 24
> and got the result "Symmetry emd_2463.map: C13, center 64 64 37"
>
> Increasing the number of sampling points does not change the result, but
> if I increase the correlation criteria a little, to say 0.992, I get the expected C12 symmetry.
> Also if I change the contour level to 0.05, the author recommended level, I get C12 again.
>
> Looking at the volume at several different contour levels, it is difficult to see how it could be considered C13, and also how it would go from C13 to C12.
>
> Kind Regards,
> Ingvar Lagerstedt
> --
> Ingvar Lagerstedt
> European Bioinformatics Institute (EMBL-EBI)
> European Molecular Biology Laboratory
> Wellcome Trust Genome Campus
> Hinxton
> Cambridge CB10 1SD
>
> Tel: +44 (0)1223 492533
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