[Chimera-users] Surprising "measure symmetry" result

[ingvar]

Hi Tom,

Thank you for the thorough answer.  It was really useful to see all the 
correlation coefficients.

EMDB has started to collect any imposed symmetry in the image 
processing, but most entries in the archive do not have that info.  One 
idea is to try remediate the older entries with the symmetries reported 
by Chimera, and I picked this entry as a spot check.  For this volume 
the authors reported that they imposed C12 symmetry, so I wanted to see 
if that was what Chimera reported.  When I viewed the volume it looked 
to me that there were some features that was C4 rather then C12, so it 
was nice to see that the cc for C4 was higher than C12, but not 
massively so.

I agree that just taking the highest cc is likely to not be the best 
choice.  One could device a significance score, maybe log(1-cc) and say 
that the lower symmetry is the relevant one if the difference is larger 
than log(2).  (There may be a better value than log(2), possibly based 
on the symmetry multiples between the two cases.)  With these rules C12 
would be favoured over C24 and also just pip C4, but a larger sampling 
set would be needed to see if this actually works.
This type of score would only apply in a relatively narrow band, we are 
only interested if the correlation is high enough, > 0.99, and there 
will be an upper limit were the values of a handful of voxels would be 
all decisive.

Another observation is that the cc is quite large for both C11 and C13. 
I think that is probably the case for any large n, if the cc for Cn is 
high then the cc's for both Cn-1 and Cn+1 are likely to also be quite 
high.

All the best,
Ingvar

On 2014-04-04 19:13, Tom Goddard wrote:
> 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
> 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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>> Chimera-users mailing list
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>> 

-- 
Ingvar Lagerstedt
European Bioinformatics Institute (EMBL-EBI)
European Molecular Biology Laboratory
Wellcome Trust Genome Campus
Hinxton
Cambridge CB10 1SD

Tel: +44 (0)1223 492533