> -----Original Message----- > From: owner-ccp...@jiscmail.ac.uk > [mailto:owner-ccp...@jiscmail.ac.uk] On Behalf Of James Holton > Sent: 21 January 2010 08:39 > To: CCP4BB@jiscmail.ac.uk > Subject: Re: [ccp4bb] Refining against images instead of only > reflections > > It is interesting and relevant here I think that if you measure > background-subtracted spot intensities you actually are measuring the > AVERAGE electron density. Yes, the arithmetic average of all > the unit > cells in the crystal. It does not matter how any of the > vibrations are > "correlated", it is still just the average (as long as you > subtract the > background). The diffuse scatter does NOT tell you about the > deviations > from this average; it tells you how the deviations are > correlated from > unit cell to unit cell.
James, as I've pointed out before this is completely inconsistent with both established DS theory and many experiments performed over the years. If you're simulation is producing this result, then the obvious conclusion is that you're not simulating what you claim to be. I don't know of a single experimental result that supports your claim. In order for it to be true the total background (i.e. the sum of the detector noise, air scatter, scattering from the cryobuffer, Compton scattering from the crystal and of course the diffuse scattering itself) would have to be a linear function (or more precisely planar since the detector co-ords are obviously 2-D) of the detector co-ordinates in the region of the Bragg spots, since that is the background model that is used for background subtraction. Whilst it may be true that detector noise and non-crystalline scattering can be accurately modeled by a linear background model (at least in the local region of each Bragg spot), this cannot possibly be generally true of the DS component, and since getting at the DS component is the whole purpose of the experiment, it is crucial that this be modeled accurately. Of course your claim may well be true if there's no DS, but we're talking specifically about cases where there is observable DS (otherwise what's the point of your simulation?). The reason it can't be true that the DS is a linear function is that there's a wealth of simulation work and experimental data that demonstrate that it's not true (not to mention simple manual observation of the images!). The simulations cannot easily be dismissed as unrealistic because in many cases they give an accurate fit to the experimental data. As an example see here: http://journals.iucr.org/a/issues/2008/01/00/sc5007/sc5007.pdf . Looking at the various simulations here (Figs 3 & 5) it's obvious that the DS is very non-linear at the Bragg positions (and more importantly it's also non-linear between the Bragg positions). Note that the simulated calculated patterns here contain no Bragg peaks since as noted in the Figure legends, the average structure (or the average density) has been subtracted in the calculation, i.e. the simulations are showing only the DS component. I fail to see how any kind of background subtraction model could cope with the DS and give the right answer for the Bragg intensity in these kind of cases. Even from the observed patterns it's plain that the DS is non-linear, and therefore a linear background correction couldn't possibly correct the raw integrated intensity for the DS component. Well-established theory says that the total coherent scattered intensity is proportional to (~=) the time-average of the squared modulus of the structure factor of the crystal: I(coherent) ~= <|Fc|^2> If we make the assumption that the deviations of the contributions to the structure factor from different unit cells are uncorrelated, we can show that the Bragg intensity is the squared modulus of the time and lattice-averaged SF sampled at the reciprocal lattice points: I(Bragg) ~= |<F>|^2 The time/lattice-averaged SF is the FT of the average density, and therefore I(Bragg) indeed corresponds to the average density. The diffuse intensity is the difference between these: I(diffuse) = I(coherent) - I(Bragg) ~= <|F|^2> - |<F>|^2 The assumption above implies that we're assuming that there's no 'acoustic' component of the DS, since this arises from correlations between different unit cells. However this doesn't mean that there *is* no acoustic component, it simply means that we are ignoring it: for one thing we have no alternative since the acoustic and Bragg scattering are practically inseparable; for another, correlations between different unit cells are purely an artifact of the crystallisation process, so have no biological significance, hence we're usually not interested in them anyway. > The diffuse scatter does NOT tell you about the deviations > from this average; it tells you how the deviations are > correlated from unit cell to unit cell. This is completely wrong, the previous equation can be rewritten as: I(diffuse) = <|F - <F>|^2> clearly demonstrating that the DS does indeed tell you about the mean-squared deviation of the SF from the average (i.e. the variance of the SF), and therefore the density from its time/lattice average. Note that I(diffuse) must necessarily be positive implying that the measured intensity always overestimates the Bragg intensity; it cannot average out to zero. If we further assume the usual harmonic model for the atomic displacements, we can show that the DS intensity is related to the covariance (or less correctly the correlation) of the displacements: I suspect this is what you meant. This is all nicely explained in Michael Wall's doctorate thesis which is available online: http://lunus.sourceforge.net/Wall-Princeton-1996.pdf . This also has a nice historical survey of all PX DS results obtained up until 1996. Cheers -- Ian Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing i.tic...@astex-therapeutics.com and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674
