[Biopython] geometry.py

[Frederico Moraes Ferreira]

Dear Ezgi,
Thanks for your explanation and references. Here goes calculations for 
the same pdb set from my previous message.
I haven't read the references yet. However, according to João's 
definition, if the semi-axis are the ones from the smallest ellipsoid 
that fits the pdb, we agree at least one of the axes have necessarily to 
match Dmax. Otherwise, there are some atoms outside the ellipsoid, in 
which case is against the primary definition.
If your interest, we can stay in touch and discuss this matter a bit more.
All the best,
Fred

P.S.: semi-axes not doubled!
##############################################
S_1AVSA_29_0004_1.pdb
#Dimensions(a,b,c) #Rg #Anisotropy
8.12 16.99 38.02 42.43 0.51
Dmax: 133.07

S_1AVSA_29_0004_10.pdb
#Dimensions(a,b,c) #Rg #Anisotropy
8.30 11.77 13.97 20.06 0.07
Dmax: 70.58

S_1AVSA_29_0004_11.pdb
#Dimensions(a,b,c) #Rg #Anisotropy
8.71 11.79 18.33 23.47 0.18
Dmax: 105.00

S_1AVSA_29_0004_12.pdb
#Dimensions(a,b,c) #Rg #Anisotropy
8.18 12.15 28.44 31.99 0.47
Dmax: 104.18

S_1AVSA_29_0004_13.pdb
#Dimensions(a,b,c) #Rg #Anisotropy
7.41 11.69 17.08 21.99 0.19
Dmax: 81.21

S_1AVSA_29_0004_14.pdb
#Dimensions(a,b,c) #Rg #Anisotropy
8.84 12.17 27.24 31.11 0.43
Dmax: 104.17

S_1AVSA_29_0004_15.pdb
#Dimensions(a,b,c) #Rg #Anisotropy
10.23 12.39 18.6 24.58 0.13
Dmax: 84.32

S_1AVSA_29_0004_16.pdb
#Dimensions(a,b,c) #Rg #Anisotropy
7.62 11.89 39.43 41.89 0.69
Dmax: 131.53

S_1AVSA_29_0004_17.pdb
#Dimensions(a,b,c) #Rg #Anisotropy
7.10 16.62 22.68 28.99 0.23
Dmax: 90.38

S_1AVSA_29_0004_18.pdb
#Dimensions(a,b,c) #Rg #Anisotropy
8.73 11.69 20.16 24.89 0.24
Dmax: 89.03

S_1AVSA_29_0004_19.pdb
#Dimensions(a,b,c) #Rg #Anisotropy
6.97 11.02 16.6 21.11 0.2
Dmax: 75.23
#############################################


Em 06-06-2012 07:51, ezgi karaca escreveu:
> Hello Frederico,
>
> In the code, we had a small scaling error and a typo, they are fixed
> right now. You can get the current version from the same link:
> http://nmr.chem.uu.nl/~joao/f/geometry.py
>
> Just to make things clear, this is how we calculate the dimensions:
>
> 1. We calculate the gyration tensor of the protein (the geometrical
> one, we don't consider the masses)
>
> 2. We diagonalize the gyration tensor and get the eigenvalues of it
>
> 3. We take the square roots of the eigenvalues, and those correspond
> to the length of the semi-axis of ellipsoid
>
> We got this procedure from the following reference: *Vondrasek J
> (2011) Gyration- and Inertia-Tensor-Based Collective Coordinates for
> Metadynamics. Application on the Conformational Behavior of
> Polyalanine Peptides and Trp-Cage Folding - The Journal of Physical
> Chemistry A*
>
>   As João has indicated, Dmax and the maximum axis length should not be
> exactly the same, since we average out the coordinates while
> calculating the gyration tensor. But, of course they should at least
> be close to each other. So, please test the current version to see how
> well it matches with your calculations and hopefully this version will
> give us more reasonable results!
>
> Cheers,
>
> Ezgi
>
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