Re: [ccp4bb] normalization of B-factor values from different crystal structures

[Daniel M. Himmel]

Dear Asmita, (and all who may be interested)

In Gourinath & Himmel et al. Structure 11:1621-1627 (2003), I normalized 
B-factors 
of several crystal structures for comparisons, using a simple applications of 
statistics.  
Any such analysis must be viewed with caution, of course, because it relies on 
the 
assumption that the crystal structures in question were well-refined with 
little model 
bias.  Otherwise, it may be useful set all B-factors in a structure to one 
value (well 
below the average B, since B-factors tend to refine up much more easily than 
refining 
down) and run through a round of refinement in which B-factors are the last 
parameter 
refined.  Then, normalize and do the comparison.  

In my case, I looking at how the difference between B-factors of one particular 
helix 
(the "SH1 Helix") and the whole structure changed over several different 
conformations 
of the protein, and I had to look at a variety of crystal structures to do the 
comparison 
and demonstrate a possible trend.

I hope this helps.

-Daniel M. Himmel

Re: [ccp4bb] normalization of B-factor values from different crystal structures

[Pavel Afonine]

Hi,

also keep in mind that the total model structure factor used in refinement
and anywhere where model-to-data agreement needs to be evaluated (such as
maps or R factors) is:

Fmodel = ktotal * (Fcalc_atoms + F_bulk_solvent + F_something_else)

where ktotal ~ scale * exp(-h*Uoverall*h_transpose) .

This makes it obvious that B factor is arbitrarily shared between Uoverall
matrix and atomic B factor.
phenix.refine subtracts as much as possible from the trace of Uoverall and
adds that to atomic B; however, sometimes it is only possible to add a part
of what can be removed from Uoverall.

With this in mind and as James pointed out, atomic B factors are likely
defined up to a constant.

Pavel


On Wed, Aug 2, 2017 at 5:54 PM, James Holton 
wrote:

> Woops, sorry.  There was a typo in my response.  here it is again without
> the typo.
>
> B factors are 78.96x the value of the mean square variation in an atom's
> position.  The square is the important part of how you scale them.  Lets
> say you have static disorder in the crystal lattice, and that gives every
> atom an rms variation of 0.5 A relative to their ideal lattice positions,
> then that static disorder imparts a B factor of 78.96*(0.5)^2 = 19.7 to all
> atoms.  If in addition to lattice disorder you have a side chain flapping
> in the breeze by another rms 1.0 A, that is B = 79, but the combination of
> the two things is an rms fluctuation of sqrt(0.5^2 + 1.0^2) = 1.118 rms A,
> and the total B factor resulting from that is 98.7.  It is not a
> coincidence that 98.7 is the sum of 19.7 and 79.  That is, independent
> sources of disorder _add_ when it comes to the B factors they produce.
>
> So, if you want to "normalize" B factors from one structure to another,
> the best thing to do is subtract a constant.  This is mathematically
> equivalent to "deconvoluting" one source of overall variation from the
> site-to-site differences.  What should the constant be?  Well, the
> structure-wide atomic B factor average isn't a bad choice.  The caveat is
> that a B factor change of 5 in the context of an overall B of 15 is
> probably significant, but in a low resolution structure with an overall B
> factor of 100, it might be nothing more than a random fluctuation.  It's
> like looking at the width of bands on a gel.  A small change in a sharp
> band is significant, but that same change in position for a fat band is
> more dubious.
> Now, crystallographically, all a B factor is is the rate of falloff of the
> contribution of an atom to the diffraction pattern with increasing
> resolution.  So, the overall B factor can be quite well known, but the B
> factor of a single atom in the context of tens of thousands of others can
> be harder to determine.  Refinement programs do their best finding the best
> fit, but in the end you are trying to reconcile a lot of different possible
> contributors to the fall-off of data with resolution.  Because of phases, a
> small change in one B factor can cancel a small change in another.  This is
> why B factor refinement at low resolution is dangerous.
>
> If you want to compare B factors I'd recommend putting "error bars" on
> them.  That is, re-refine the structures of interest after jiggling the
> coordinates and setting all the B factors to a constant.  See how
> reproducible the final B factors are.  This will give you an idea of how
> big a change can happen by pure random chance, even with the same data.
>
> Hope that helps!
>
> -James  Holton
> MAD Scientist
>
> On 8/2/2017 12:09 PM, Asmita wrote:
>
> Hi,
>
> This might look as a very fundamental question. I have a dataset of
> crystal structures better than 3.5Ang resolution. For a qualitative
> analysis, I want to compare the residue-wise B-factors in these structures,
> but due to different procedures adopted in refinement and scaling, I
> understand that these values cannot be compared in a raw manner.
>
> Can someone suggest appropriate normalization methods that could be used
> for scaling these B-factors for a relevant and meaningful comparison? All
> the files have isotropic B-factor values and there are no ANISOU entries in
> any of the files.
>
> Thanks
>
> Asmita
>
>
>

Re: [ccp4bb] normalization of B-factor values from different crystal structures

[James Holton]

Woops, sorry.  There was a typo in my response.  here it is again 
without the typo.


B factors are 78.96x the value of the mean square variation in an atom's 
position.  The square is the important part of how you scale them.  Lets 
say you have static disorder in the crystal lattice, and that gives 
every atom an rms variation of 0.5 A relative to their ideal lattice 
positions, then that static disorder imparts a B factor of 78.96*(0.5)^2 
= 19.7 to all atoms. If in addition to lattice disorder you have a side 
chain flapping in the breeze by another rms 1.0 A, that is B = 79, but 
the combination of the two things is an rms fluctuation of sqrt(0.5^2 + 
1.0^2) = 1.118 rms A, and the total B factor resulting from that is 
98.7.  It is not a coincidence that 98.7 is the sum of 19.7 and 79.  
That is, independent sources of disorder _add_ when it comes to the B 
factors they produce.


So, if you want to "normalize" B factors from one structure to another, 
the best thing to do is subtract a constant.  This is mathematically 
equivalent to "deconvoluting" one source of overall variation from the 
site-to-site differences.  What should the constant be?  Well, the 
structure-wide atomic B factor average isn't a bad choice.  The caveat 
is that a B factor change of 5 in the context of an overall B of 15 is 
probably significant, but in a low resolution structure with an overall 
B factor of 100, it might be nothing more than a random fluctuation.  
It's like looking at the width of bands on a gel.  A small change in a 
sharp band is significant, but that same change in position for a fat 
band is more dubious.


Now, crystallographically, all a B factor is is the rate of falloff of 
the contribution of an atom to the diffraction pattern with increasing 
resolution.  So, the overall B factor can be quite well known, but the B 
factor of a single atom in the context of tens of thousands of others 
can be harder to determine.  Refinement programs do their best finding 
the best fit, but in the end you are trying to reconcile a lot of 
different possible contributors to the fall-off of data with 
resolution.  Because of phases, a small change in one B factor can 
cancel a small change in another.  This is why B factor refinement at 
low resolution is dangerous.


If you want to compare B factors I'd recommend putting "error bars" on 
them.  That is, re-refine the structures of interest after jiggling the 
coordinates and setting all the B factors to a constant.  See how 
reproducible the final B factors are.  This will give you an idea of how 
big a change can happen by pure random chance, even with the same data.


Hope that helps!

-James  Holton
MAD Scientist

On 8/2/2017 12:09 PM, Asmita wrote:

Hi,

This might look as a very fundamental question. I have a dataset of 
crystal structures better than 3.5Ang resolution. For a qualitative 
analysis, I want to compare the residue-wise B-factors in these 
structures, but due to different procedures adopted in refinement and 
scaling, I understand that these values cannot be compared in a raw 
manner.


Can someone suggest appropriate normalization methods that could be 
used for scaling these B-factors for a relevant and meaningful 
comparison? All the files have isotropic B-factor values and there are 
no ANISOU entries in any of the files.


Thanks

Asmita

Re: [ccp4bb] normalization of B-factor values from different crystal structures

[James Holton]

B factors are 78.96x the value of the mean square variation in an atom's 
position.  The square is the important part of how you scale them.  Lets 
say you have static disorder in the crystal lattice, and that gives 
every atom an rms variation of 0.5 A relative to their ideal lattice 
positions, then that static disorder imparts a B factor of 78.96*(0.3)^2 
= 19.7 to all atoms. If in addition to lattice disorder you have a side 
chain flapping in the breeze by another rms 1.0 A, that is B = 79, but 
the combination of the two things is an rms fluctuation of sqrt(0.5^2 + 
1.0^2) = 1.118 rms A, and the total B factor resulting from that is 
98.7.  It is not a coincidence that 98.7 is the sum of 19.7 and 79.  
That is, independent sources of disorder _add_ when it comes to the B 
factors they produce.


So, if you want to "normalize" B factors from one structure to another, 
the best thing to do is subtract a constant.  This is mathematically 
equivalent to "deconvoluting" one source of overall variation from the 
site-to-site differences.  What should the constant be?  Well, the 
structure-wide atomic B factor average isn't a bad choice.  The caveat 
is that a B factor change of 5 in the context of an overall B of 15 is 
probably significant, but in a low resolution structure with an overall 
B factor of 100, it might be nothing more than a random fluctuation.  
It's like looking at the width of bands on a gel.  A small change in a 
sharp band is significant, but that same change in position for a fat 
band is more dubious.


Now, crystallographically, all a B factor is is the rate of falloff of 
the contribution of an atom to the diffraction pattern with increasing 
resolution.  So, the overall B factor can be quite well known, but the B 
factor of a single atom in the context of tens of thousands of others 
can be harder to determine.  Refinement programs do their best finding 
the best fit, but in the end you are trying to reconcile a lot of 
different possible contributors to the fall-off of data with 
resolution.  Because of phases, a small change in one B factor can 
cancel a small change in another.  This is why B factor refinement at 
low resolution is dangerous.


If you want to compare B factors I'd recommend putting "error bars" on 
them.  That is, re-refine the structures of interest after jiggling the 
coordinates and setting all the B factors to a constant.  See how 
reproducible the final B factors are.  This will give you an idea of how 
big a change can happen by pure random chance, even with the same data.


Hope that helps!

-James  Holton
MAD Scientist

On 8/2/2017 12:09 PM, Asmita wrote:

Hi,

This might look as a very fundamental question. I have a dataset of 
crystal structures better than 3.5Ang resolution. For a qualitative 
analysis, I want to compare the residue-wise B-factors in these 
structures, but due to different procedures adopted in refinement and 
scaling, I understand that these values cannot be compared in a raw 
manner.


Can someone suggest appropriate normalization methods that could be 
used for scaling these B-factors for a relevant and meaningful 
comparison? All the files have isotropic B-factor values and there are 
no ANISOU entries in any of the files.


Thanks

Asmita

Re: [ccp4bb] normalization of B-factor values from different crystal structures

[Avinash Punekar]

Hi Asmita,

Try running your different crystal structures through PDB_REDO. That should 
normalize the B-factors to some meaningful values for comparison.

Best wishes,
Avinash

Re: [ccp4bb] normalization of B-factor values from different crystal structures

[Ethan A Merritt]

On Wednesday, 02 August, 2017 21:58:07 Asmita Gupta wrote:
> Hi,
> 
> Thanks for the response! 
> 
> What I have are crystal structures of the same protein in multiple 
> conformations, solved by different groups. I wanted to calculate the 
> residue-wise B-factors for each of these structures and compare how the 
> values are changing for corresponding residues in these different structures. 
> e.g. B-factor variation in residue number 200 (Ala) in 10 different 
> conformations of a protein. 
> 
> Hope I have been able to answer the question!

But what is the biological question?  
You haven't learned much if all you can say is
"The B factor of residue 200 is higher in this structure".

Do you not have a larger question in mind - on the order
of "ligand binding a site X correlates with reduced 
mobility of loop A-B"?   

For such questions I suggest (as I always do :-) using TLSMD
analysis rather than examining individual B factors.  
That allows you to say something like "in structure #1 we
can identify a distinct group motion of residues in loop A-B,
whereas in structure #2 loop A-B appears to move in concert
with the entire subdomain XX".  This is not the same thing
as saying individual B factors are higher or lower.

Ethan

-- 
Ethan A Merritt
Biomolecular Structure Center,  K-428 Health Sciences Bldg
MS 357742,   University of Washington, Seattle 98195-7742

Re: [ccp4bb] normalization of B-factor values from different crystal structures

[Asmita Gupta]

Hi,

Thanks for the response! 

What I have are crystal structures of the same protein in multiple 
conformations, solved by different groups. I wanted to calculate the 
residue-wise B-factors for each of these structures and compare how the values 
are changing for corresponding residues in these different structures. e.g. 
B-factor variation in residue number 200 (Ala) in 10 different conformations of 
a protein. 

Hope I have been able to answer the question!

Re: [ccp4bb] normalization of B-factor values from different crystal structures

[Ethan A Merritt]

On Wednesday, 02 August, 2017 12:09:35 Asmita wrote:
> Hi,
> 
> This might look as a very fundamental question. I have a dataset of crystal
> structures better than 3.5Ang resolution. For a qualitative analysis, I
> want to compare the residue-wise B-factors in these structures, but due to
> different procedures adopted in refinement and scaling, I understand that
> these values cannot be compared in a raw manner.
> 
> Can someone suggest appropriate normalization methods that could be used
> for scaling these B-factors for a relevant and meaningful comparison? All
> the files have isotropic B-factor values and there are no ANISOU entries in
> any of the files.

I may have an answer, but I first I need a better handle on the question.

Can you take a step back and explain what question or hypothesis you
would like to address by making the comparison?  

Do you want to compare B factors for different residues in the same structure,
or B factors for the same residue in different structures,
or something else entirely?

Ethan

-- 
Ethan A Merritt
Biomolecular Structure Center,  K-428 Health Sciences Bldg
MS 357742,   University of Washington, Seattle 98195-7742