At the limit, the microdomain picture leads to powder-diffraction-type spots (rings), provided the block size is relatively large with respect to the unit cell. And as the blocks get smaller, the distinction between "changing unit cell parameters" and "mosaic block misorientation" dissolves.
I am wondering, then, what one explains by positing microdomains, actually? Is there strong evidence supporting their existence?
JPK
-----Original Message-----
From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of Colin Nave
Sent: Thursday, March 13, 2014 7:04 PM
To: [log in to unmask]
Subject: Re: [ccp4bb] twinning problem ?
Hi Zbyszek
I think this has deviated significantly from twinning problems!
I certainly don't claim the 1998 study was typical. The crystal was large by present day standards, no cryoprotectant was used and non uniform drying/cooling rates might have occurred.
The Juers et. al. paper includes the statement "However, in most cases [omega] does not dominate, suggesting that [delta]a/a plays a significant role in nearly all of our samples."
There is also the Kriminski paper (http://journals.iucr.org/d/issues/2002/03/00/en0056/index.html) which includes the statement " Flash-cooling tetragonal lysozyme crystals degrades diffraction resolution and broadens the distributions of lattice orientations (mosaicity) and lattice spacings. The diffraction resolution strongly correlates with the width of the lattice-spacing distribution."
The Diedrichs paper includes "The experience of the author is that for most protein crystals reflections are not markedly elongated along circles corresponding to their d-spacing; therefore, `rotational mosaicity' appears to play a minor role ..... the model calculations suggest that, apart from inhomogeneity and disorder in unit cells, unit-cell parameter variations are responsible for most of the imperfections that result in poor diffraction properties of crystals.
Of course selectively quoting papers can be misleading!
Fig. 5A of Juers et al lumps omega and delta a/a together and does not distinguish between the two. The plot is [eta] versus d. The slope of a line fit to this plot gives an estimate of 1/s, while the y intercept estimates [omega] + [delta]a/a. In this case, s is the mosaic block size.
To summarise cryocooling can produce a fragmentation in to smaller mosaic blocks with larger angular variation between blocks and a distribution of cell dimensions between blocks and within blocks (elastic strain). It really needs a high resolution diffraction set up (to detect diffracted beam divergences above those given by the incident beam divergence) to distinguish between the various effects.
Of course, in some cases, such a set up could reveal certain types of twinning (so I have left the subject of the email unchanged!)
Regards
Colin
-----Original Message-----
From: Zbyszek Otwinowski [mailto:[log in to unmask]]
Sent: 13 March 2014 21:33
To: ccp4bb
Subject: Re: [ccp4bb] twinning problem ?
On 03/13/2014 10:55 AM, Keller, Jacob wrote:
>> Unless you are interested in finding curious objects, what would you do with protein quasicrystal? The practices of macromolecular crystallography is about determining 3-dimensional structure of objects being crystallized. Protein quasicrystal are really unlikely to diffract to high enough resolution, and even ignoring all other practical aspects, like writing programs to solve such a structure, chances of building an atomic model are really slim.
>
> Right, if crystallography is seen as purely a tool for biology I agree. As for curious objects, I think almost all profound breakthroughs come from unadulterated curiosity and not desire for some practical end. Not sure why a priori this should be so, but just consider your favorite scientific breakthrough and whether the scientist set out to make the discovery or not. Some are, but most are not, I think. Maybe aperiodic protein crystals have some important function in biology somewhere, or have unforeseen materials science properties, analogous to silk or something.
>
>>> This is easy to test by analyzing diffraction patterns of individual crystals.
>> In practice, the dominant contribution to angular broadening of
>> diffraction peaks is angular disorder of microdomains, particularly in cryo-cooled crystals.
>> However, exceptions do happen, but these rare situations need to be
>> handled on case by case basis.
>> The interpretation of the data presented in this article is that variation in unit cell between microcrystals induce their spatial misalignment. The data do not show variation of unit cell within individual microscrystalline domains.
>> Tetragonal lysozyme can adopt quite a few variations of the crystal lattice during cryocooling. Depending on the conditions used, resulting mosaicity can vary from 0.1 degree (even for 1mm size crystal) to over 1. degree.
> Consequently, measured structure factors from a group of tetragonal lysozyme crystal can be quite reproducible, or not. As a test crystal, it should be handled with care.
> 1 degree mosaicity is not an impediment to high quality measurements. However, high mosaicity tends to correlate with presence of phase transitions during cryo-cooling. If such transition happen during cryo-cooling, crystals of the same protein, even from the same drop, may vary quite a lot in terms of structure factors. Additionally, even similar values of unit cell parameters are not guarantee of isomorphism between crystals.
>
> So I think you are saying that tetragonal lysozyme is an atypical case, and that normally the main contributor to the fitted parameter "mosaicity" is the phenomenon of microdomains shifted slightly in orientation. Maybe we can get the author to repeat the study for the other usual-suspect protein crystals to find out the truth, but the score currently seems to be 1-0 in favor of cell parameter shifts versus microcrystal orientation...
>
No, I claim that the particular crystal studied by Colin Nave (Acta Cryst. 1998,
D54: 848) is atypical case. I processed myself hundreds of tetragonal lysozyme data sets acquired on crystals grown and mounted by various people, so I believe that my experience defines better a typical case.
The second reference, nicely provided by Colin, does not make the conclusion that "dominant imperfection appeared to be a variation in unit-cell dimensions in the crystal", but rather states that "The analysis further suggests that LT disorder is governed by variability inherent in the cooling process combined with the overall history of the crystal."
As you can see on the figure 5A in Juers at al, 2007, the mosaicity is a dominant component of the reflection width for resolution higher than 8A.
Only for very low resolutions one can see the effect of unit cell changes.
What is important is that the crystal analyzed had a very low mosaicity: less than 0.02 degree before cryo-cooling and less than 0.1 degree after cryo-cooling. The mosacity after cryo-cooling is definitely below typical values.
One has to remember that not only unit cell parameters are different for different microdomains, but also their structure factors will vary and can change quite a lot. Cryo-cooled crystals definitely can have high degree of internal non-isomorphism resulting from this effect.
Zbyszek
--
Zbyszek Otwinowski
UT Southwestern Medical Center
5323 Harry Hines Blvd., Dallas, TX 75390-8816
(214) 645 6385 (phone) (214) 645 6353 (fax) [log in to unmask]
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