Re: [ccp4bb] (EXTERNAL) Re: [ccp4bb] acceptable difference between Average B-factor and Wilson B

2019-03-12 Thread Dale Tronrud 
   I agree completely!  The higher resolution data is determined
entirely by the atoms with low B factor.  If fact, the Wilson B plots
I've seen have a distinct curve to them -- They are not straight lines.
 As one looks to higher and higher resolution the curve gets shallower
and shallower.  You can actually see the population of atoms
contributing to each increasing resolution has a lower and lower average B.

Dale Tronrud

On 3/12/2019 2:24 PM, Edward A. Berry wrote:
> What if you have one domain with many B-factors aroun 70 and above, and
> another domain with B-factors around 20? The atoms with high B-factor
> will make essentially no contribution to the intensty of spots beyond 3
> A, and so have no effect on the slope of the Wilson plot byond that. But
> they will contribute mightily to the average atomic B. Or so it seems to
> me.
> eab
> 
> On 03/12/2019 04:39 PM, DUMAS Philippe (IGBMC) wrote:
>>
>> Le Mardi 12 Mars 2019 19:55 CET, Dale Tronrud 
>> a écrit:
>>
>> Dale
>> Good to have the opportunity of going back to the crystallography of
>> the fifties in these post-modern times...
>> There is an essential argumentation that should be recalled. The only
>> reason for the fact that one ignores low-resolution data in a Wilson
>> plot is that a Wilson plot is based precisely upon Wilson statistics,
>> which assumes that the atoms are cast randomly in the unit cell.
>> This assumption obviously does not hold at low resolution and there is
>> no reason to obtain a straight line that stems from the latter
>> assumption.
>> Therefore, I do not think one may say that a Wilson plot tends to
>> ignore atoms with high B values.
>> Consequence: if one has data at rather low resolution, a Wilson plot
>> is inherently inaccurate, but if one has data at very high resolution,
>> the Wilson plot should give a very decent estimate of the average B
>> and any significant discrepancy should ring the bell.
>> Philippe Dumas
>>
>>
>>>     The numeric average of the B factors of the atoms in your model only
>>> roughly corresponds to the calculation of the Wilson B.  While I always
>>> expect the average B to be larger than the Wilson B, how much larger
>>
>>> depends on many factors, making it a fairly useless criteria for judging
>>> the correctness of a model.
>>>
>>>     While it is pretty easy to understand the average of the B
>>> factors in
>>> your model, the Wilson B is more difficult.  Since it is calculated by
>>> drawing a line though the (Log of) the intensity of your structure
>>> factors as a function of the square of sin theta over lambda, it is
>>> rather removed from the atomic B factors.  When drawing the line the low
>>> resolution data are ignored because those data don't fall on a straight
>>> line, and this means that the large B factor atoms in your model are
>>
>>> ignored in the Wilson B calculation.
>>>
>>>     The Wilson B is (sort of) a weighted average of the B factors of
>>> your
>>> model, with the smallest B's given the largest weight.  The actually
>>
>>> weighting factor is a little obscure so I don't know how to simulate it
>>> to adjust the averaging of atomic B's to come out a match.  The easiest
>>> way to compare your model to the Wilson B is to calculate structure
>>> factors from it and calculate the Calculated Wilson B.  No one does this
>>> because it will always come out as a match.  If your calculated Wilson B
>>> doesn't match the observed Wilson B your R values are guaranteed to be
>>> unacceptable and your refinement program will have to be malfunctioning
>>> to create such a model.
>>>
>>>     If all the B factors in your model are equal to each other, your
>>> refined model will have an average B that matches the Wilson B, because
>>> weighting doesn't matter in that situation.  If you allow the B's to
>>
>>> vary, the difference between the average and the Wilson B will depend on
>>> how high of an individual B factor you are willing to tolerate.  If you
>>> are a person who likes to build chain into weak loops of density, or
>>
>>> build side chains where there is little to no density, then your average
>>> B will be much larger than the Wilson B.  This does not mean there is an
>>> error, it is simply a reflection of the Wilson B's insensitivity to
>>> atoms with large B.
>>>
>>>     I do not believe comparing the average B to the Wilson B has any
>>> utility at all.
>>>
>>> Dale Tronrud
>>>
>>> On 3/12/2019 11:34 AM, Eze Chivi wrote:
 Dear CCP4bb community,


 The average B-factor (calculated from model) of my protein is 65,
 whereas the Wilson B is 52. I have read in this BB that "it is expected
 that average B does not deviate strongly from the Wilson B". How I can
 evaluate if the difference calculated for my data is razonable or not?


 Thank you in advance


 Ezequiel


 


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Re: [ccp4bb] (EXTERNAL) Re: [ccp4bb] acceptable difference between Average B-factor and Wilson B

2019-03-12 Thread Ian Tickle 
Hi Edward

This is because taking a naive straight arithmetic average of the B factors
as all the programs do is nonsense!  To simplify your argument say we have
just 2 atoms with B = 10 and 1000.  What's the average B?  Answer: not 505
but very close to 10 because the atom with B=1000 most likely isn't there.
So you need an average weighted by the contribution to the scattering over
the resolution range.  This is effectively what the Wilson plot is doing:
it is certainly not performing a naive arithmetic average.  So if you're
going to compare it, at least compare it with the right quantity, though
I'm not claiming that this will give you better agreement between the
weighted average & Wilson Bs, for reasons mentioned by others.

For a possible solution see: Acta Cryst. 
 (1998). D*54* , 243-252
(shameless plug).

Cheers

-- Ian

On Tue, 12 Mar 2019 at 21:24, Edward A. Berry  wrote:

> What if you have one domain with many B-factors aroun 70 and above, and
> another domain with B-factors around 20? The atoms with high B-factor will
> make essentially no contribution to the intensty of spots beyond 3 A, and
> so have no effect on the slope of the Wilson plot byond that. But they will
> contribute mightily to the average atomic B. Or so it seems to me.
> eab
>
> On 03/12/2019 04:39 PM, DUMAS Philippe (IGBMC) wrote:
> >
> > Le Mardi 12 Mars 2019 19:55 CET, Dale Tronrud  a
> écrit:
> >
> > Dale
> > Good to have the opportunity of going back to the crystallography of the
> fifties in these post-modern times...
> > There is an essential argumentation that should be recalled. The only
> reason for the fact that one ignores low-resolution data in a Wilson plot
> is that a Wilson plot is based precisely upon Wilson statistics, which
> assumes that the atoms are cast randomly in the unit cell.
> > This assumption obviously does not hold at low resolution and there is
> no reason to obtain a straight line that stems from the latter assumption.
> > Therefore, I do not think one may say that a Wilson plot tends to ignore
> atoms with high B values.
> > Consequence: if one has data at rather low resolution, a Wilson plot is
> inherently inaccurate, but if one has data at very high resolution, the
> Wilson plot should give a very decent estimate of the average B and any
> significant discrepancy should ring the bell.
> > Philippe Dumas
> >
> >
> >> The numeric average of the B factors of the atoms in your model only
> >> roughly corresponds to the calculation of the Wilson B.  While I always
> >> expect the average B to be larger than the Wilson B, how much larger
> >
> >> depends on many factors, making it a fairly useless criteria for judging
> >> the correctness of a model.
> >>
> >> While it is pretty easy to understand the average of the B factors
> in
> >> your model, the Wilson B is more difficult.  Since it is calculated by
> >> drawing a line though the (Log of) the intensity of your structure
> >> factors as a function of the square of sin theta over lambda, it is
> >> rather removed from the atomic B factors.  When drawing the line the low
> >> resolution data are ignored because those data don't fall on a straight
> >> line, and this means that the large B factor atoms in your model are
> >
> >> ignored in the Wilson B calculation.
> >>
> >> The Wilson B is (sort of) a weighted average of the B factors of
> your
> >> model, with the smallest B's given the largest weight.  The actually
> >
> >> weighting factor is a little obscure so I don't know how to simulate it
> >> to adjust the averaging of atomic B's to come out a match.  The easiest
> >> way to compare your model to the Wilson B is to calculate structure
> >> factors from it and calculate the Calculated Wilson B.  No one does this
> >> because it will always come out as a match.  If your calculated Wilson B
> >> doesn't match the observed Wilson B your R values are guaranteed to be
> >> unacceptable and your refinement program will have to be malfunctioning
> >> to create such a model.
> >>
> >> If all the B factors in your model are equal to each other, your
> >> refined model will have an average B that matches the Wilson B, because
> >> weighting doesn't matter in that situation.  If you allow the B's to
> >
> >> vary, the difference between the average and the Wilson B will depend on
> >> how high of an individual B factor you are willing to tolerate.  If you
> >> are a person who likes to build chain into weak loops of density, or
> >
> >> build side chains where there is little to no density, then your average
> >> B will be much larger than the Wilson B.  This does not mean there is an
> >> error, it is simply a reflection of the Wilson B's insensitivity to
> >> atoms with large B.
> >>
> >> I do not believe comparing the average B to the Wilson B has any
> >> utility at all.
> >>
> >> Dale Tronrud
> >>
> >> On 3/12/2019 11:34 AM, Eze Chivi

Re: [ccp4bb] (EXTERNAL) Re: [ccp4bb] acceptable difference between Average B-factor and Wilson B

2019-03-12 Thread Edward A. Berry 

What if you have one domain with many B-factors aroun 70 and above, and another 
domain with B-factors around 20? The atoms with high B-factor will make 
essentially no contribution to the intensty of spots beyond 3 A, and so have no 
effect on the slope of the Wilson plot byond that. But they will contribute 
mightily to the average atomic B. Or so it seems to me.
eab

On 03/12/2019 04:39 PM, DUMAS Philippe (IGBMC) wrote:


Le Mardi 12 Mars 2019 19:55 CET, Dale Tronrud  a écrit:

Dale
Good to have the opportunity of going back to the crystallography of the 
fifties in these post-modern times...
There is an essential argumentation that should be recalled. The only reason 
for the fact that one ignores low-resolution data in a Wilson plot is that a 
Wilson plot is based precisely upon Wilson statistics, which assumes that the 
atoms are cast randomly in the unit cell.
This assumption obviously does not hold at low resolution and there is no 
reason to obtain a straight line that stems from the latter assumption.
Therefore, I do not think one may say that a Wilson plot tends to ignore atoms 
with high B values.
Consequence: if one has data at rather low resolution, a Wilson plot is 
inherently inaccurate, but if one has data at very high resolution, the Wilson 
plot should give a very decent estimate of the average B and any significant 
discrepancy should ring the bell.
Philippe Dumas



The numeric average of the B factors of the atoms in your model only
roughly corresponds to the calculation of the Wilson B.  While I always
expect the average B to be larger than the Wilson B, how much larger



depends on many factors, making it a fairly useless criteria for judging
the correctness of a model.

While it is pretty easy to understand the average of the B factors in
your model, the Wilson B is more difficult.  Since it is calculated by
drawing a line though the (Log of) the intensity of your structure
factors as a function of the square of sin theta over lambda, it is
rather removed from the atomic B factors.  When drawing the line the low
resolution data are ignored because those data don't fall on a straight
line, and this means that the large B factor atoms in your model are



ignored in the Wilson B calculation.

The Wilson B is (sort of) a weighted average of the B factors of your
model, with the smallest B's given the largest weight.  The actually



weighting factor is a little obscure so I don't know how to simulate it
to adjust the averaging of atomic B's to come out a match.  The easiest
way to compare your model to the Wilson B is to calculate structure
factors from it and calculate the Calculated Wilson B.  No one does this
because it will always come out as a match.  If your calculated Wilson B
doesn't match the observed Wilson B your R values are guaranteed to be
unacceptable and your refinement program will have to be malfunctioning
to create such a model.

If all the B factors in your model are equal to each other, your
refined model will have an average B that matches the Wilson B, because
weighting doesn't matter in that situation.  If you allow the B's to



vary, the difference between the average and the Wilson B will depend on
how high of an individual B factor you are willing to tolerate.  If you
are a person who likes to build chain into weak loops of density, or



build side chains where there is little to no density, then your average
B will be much larger than the Wilson B.  This does not mean there is an
error, it is simply a reflection of the Wilson B's insensitivity to
atoms with large B.

I do not believe comparing the average B to the Wilson B has any
utility at all.

Dale Tronrud

On 3/12/2019 11:34 AM, Eze Chivi wrote:

Dear CCP4bb community,


The average B-factor (calculated from model) of my protein is 65,
whereas the Wilson B is 52. I have read in this BB that "it is expected
that average B does not deviate strongly from the Wilson B". How I can
evaluate if the difference calculated for my data is razonable or not?


Thank you in advance


Ezequiel




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