Hi Jonathan

I think you are getting close in your analysis but still not quite there. You have to remember that the Fourier coefficient in the density equation is not the measured amplitude Fo but a weighted term to take account of the errors, i.e. 2mFo-DFc for acentrics, or mFo for centrics. Also it's not true that a zero value for F is very likely to be wrong. The Wilson distribution for an acentric F peaks at F=0, so for the prior at least, zero is the most likely value! After you have actually measured F the posterior estimate will change by an amount which depends on the relative magnitude of the experimental error, so in the case that the error is large the posterior estimate may also likely be very close to zero.

You have remember too that the structure factor is a complex number, so you have to consider the value in the complex plane, i.e. taking account of the phase, not the amplitude. Finally the refinement program will automatically down-weight low quality data via the m and D terms, so even if the amplitude isn't zero the Fourier coefficient may well end up being zero, or as near zero as makes no difference to the map (or indeed to the refinement).

Also I would take issue with your definition of 'resolution'. Actually it has a very clear definition: it's the minimum distinguishable separation of peaks in the map. One could also talk about the resolution of a diffraction image as being the smallest separation of spots that is clearly distinguishable, which will depend on the spot size and indirectly on the mosaicity and the beam divergence. In powder diffraction 'resolution' is used in the same way to refer to the minimum distinguishable separation of powder lines which depends largely on the focusing of the source, i.e. nothing whatsoever to do with the meaning of resolution used in MX!

As such, resolution is a variable as a function of position in the image, not a constant for a given dataset (so the resolution is very low in the solvent region, high in the well-ordered regions of the macromolecule and intermediate in the less-ordered regions, depending on the degree of order). This is a standard definition of resolution (or 'resolving power') used by anyone doing any kind of image processing (e.g. electron microscopy and astronomy).

What most MX crystallographers now call 'resolution' was called from the very early days of crystallography (as small-molecule crystallographers indeed still do) 'minimum d-spacing' (d_min), which is a constant for a given dataset and which has only a very tenuous relationship with the resolution - particularly if the data at low d-spacing are very poor!

Cheers

-- Ian

On 28 November 2015 at 13:39, Jonathan Brooks-Bartlett <[log in to unmask]> wrote:

Hi Talis,

I am far from a refinement expert but I'll chip in with my thoughts on why this is, which may be wrong but the worst that can happen is that someone corrects me and I learn something new.

A very simplistic and naive interpretation is that by including the data up to 1.8A you are including more information and so you are getting better information out.

But why is this the case?

The electron density equation tells us that to get the electron density at each point in space we have to sum over all of amplitudes and phases (it's a Fourier transform), so we have to make sure we obtain the correct values for these quantities to obtain the correct electron density. If you cut your data at 2.6A then you completely leave out any extra information that you obtain from reflections out to 1.8A. But the real problem with this is when it comes to the electron density equation. Any "missing" information is encoded as the amplitude being 0, which is very likely to be WRONG! So we don't treat the data as missing, we just say that the amplitude is 0.

So the reason why I think the 1.8A data is a bit better, despite worse data quality stats, is because the contribution to the electron density equation is non zero for the reflection amplitudes out to 1.8A. Although the contributions may bot be perfect (the data quality isn't great) it's a better estimate than just setting the amplitudes to zero.

This leads on to the question "what is resolution?"

My interpretation of resolution is that it is a semi-quantitative measure of the amount of terms used in the electron density equation.

So the more terms you use in the electron density equation (higher resolution), the better the electron density representation of your protein. So as long as you trust the measurements of your reflections you should use them in the processing (this is why error values are important), because otherwise you'll set the contribution in the electron density equation to 0 (which is likely to be wrong anyway).

But I would wait for a more experienced crystallographer than me confirm whether anything I've stated actually makes sense or not.

This is my 2p ;)

Jonny Brooks-Bartlett

Garman Group

DPhil candidate Systems Biology Doctoral Training Centre

Department of Biochemistry

University of Oxford

From: CCP4 bulletin board [[log in to unmask]] on behalf of Eleanor Dodson [[log in to unmask]]
Sent: 28 November 2015 13:12
To: [log in to unmask]
Subject: Re: [ccp4bb] Puzzled: worst statistics but better maps?

I am not surprised - Your CC1/2 is very high at 2.6A and there must be lots of information past that resolution..
Maybe the 1.8A cut off is unrealistic, but some of that extra data will certainly have helped ..

But the map appearance over modelled residues can be misleadingly good. Remember al the PHASES are calculated from the given model so a reflection with any old amplitude rubbish will have some signal .

A better test is to omit a few residues from the phasing and see where you get the best density for the omitted segment of the structure

Eleanor

On 28 November 2015 at 11:53, Ian Tickle <[log in to unmask]> wrote:

Hi, IMO preconceived notions of where to apply a resolution cut-off to the data are without theoretical foundation and most likely wrong. You may decide empirically based on a sample of data what are the optimal cut-off criteria but that doesn't mean that the same criteria are generally applicable to other data. Modern refinement software is now sufficiently advanced that the data are automatically weighted to enhance the effect of 'good' data on the results relative to that of 'bad' data. Such a continuous weighting function is likely to be much more realistic from a probabilistic standpoint than the 'Heaviside' step function that is conventionally applied. The fall-off in data quality with resolution is clearly gradual so why on earth should the weight be a step function?

Just my 2p.

Cheers

-- Ian

On 28 November 2015 at 11:21, Greenstone talis <[log in to unmask]> wrote:

Dear All,

I initially got a 3.0 A dataset that I used for MR and refinement. Some months later I got better diffracting crystals and refined the structure with a new dataset at 2.6 A (for this, I preserved the original Rfree set).

Even though I knew I was in a reasonable resolution limit already, I was curious and I processed the data to 1.8 A and used it for refinement (again, I preserved the original Rfree set). I was surprised to see that despite the worst numbers, the maps look better (pictures and some numbers attached).

2.6 A dataset:

Rmeas: 0.167 (0.736)

I/sigma: 9.2 (2.2)

CC(1/2): 0.991 (0.718)

Completeness (%): 99.6 (99.7)

1.8 A dataset:

Resolution: 1.8 A

Rmeas: 0.247 (2.707)

I/sigma: 5.6 (0.3)

CC(1/2): 0.987 (-0.015)

Completeness (%): 66.7 (9.5)

I was expecting worst maps with the 1.8 A dataset...any explanations would be very appreciated.

Thank you,

Talis