From: Theresa H. Hsu
Date: 9 January 2012 18:15
Dear crystallographers
A theoretical question - can sub-angstrom resolution structures only be obtained for a limited set of proteins? Is it impossible to achieve for membrane proteins and large complexes?
Theresa
----------
From: Cale Dakwar
In theory, no: sub-angstrom resolution can be obtained for any and all proteins, including membrane proteins, and for large complexes. In reality, it becomes technically very difficult to achieve; you would need ever-colder temperatures and ever-stronger irradiation sources.
----------
From: Tim Gruene
Hi,
in my opinion the resolution limit of crystals from large complexes/
membrane proteins is more likely due to lattice imperfections and
long-range disorder, and cold neither cold temperatures nor stronger
radiation sources would circumvent this problem.
Tim
Date: 9 January 2012 18:15
Dear crystallographers
A theoretical question - can sub-angstrom resolution structures only be obtained for a limited set of proteins? Is it impossible to achieve for membrane proteins and large complexes?
Theresa
----------
From: Cale Dakwar
In theory, no: sub-angstrom resolution can be obtained for any and all proteins, including membrane proteins, and for large complexes. In reality, it becomes technically very difficult to achieve; you would need ever-colder temperatures and ever-stronger irradiation sources.
P.S. In theory, the only limit to describing the location of the atoms would be described by the heisenberg uncertainty principle.
----------
From: Tim Gruene
Hi,
in my opinion the resolution limit of crystals from large complexes/
membrane proteins is more likely due to lattice imperfections and
long-range disorder, and cold neither cold temperatures nor stronger
radiation sources would circumvent this problem.
Tim
----------
From: Jacob Keller
The word "theory" in this thread/question has to be clarified better.
Jacob
----------
From: Ed Pozharski
On the matter of large proteins.
Let's say your molecule is so big, the unit cell parameters are
300x300x300 A. To obtain 1A data, you need reflections with miller
indices of ~300. For these to be measurable, you need, I presume, ~300
unit cells in each direction (otherwise you don't even have a formed
Bragg plane). 300A x 300 ~ 10^5 A, or 10 micron. So it seems to me
that with large molecules you would essentially hit the crystal size
limit. In reality, to get any decent data one would need maybe 3000
unit cells, or 100 micron crystal. While such crystals could
theoretically grow (maybe in microgravity), it is highly unlikely that
the whole crystal will be essentially a single mosaic block. Simply
because large proteins are always multi-domain, and thus too flexible.
So I'd say while everything is theoretically possible, for very large
proteins the probability of getting submicron resolution is exceedingly
small.
Cheers,
Ed.
--
Oh, suddenly throwing a giraffe into a volcano to make water is crazy?
Julian, King of Lemurs
----------
From: Ethan Merritt
The ground-breaking work by Chapman et al. using the Stanford FEL to
record diffraction from nanocrystals of Photosystem II would seem to
constitute an encouraging counter-example
Nature [2011] doi:10.1038/Nature09750
It remains to be seen what resolution might ultimately be achieved by
nanocrystal experiments. As I understand it, the resolution of the
work to date has been limited by the apparatus rather than by the crystals.
Ethan
--
Ethan A Merritt
----------
From: Colin Nave
Yes, I think Ed's analysis is a bit misleading. If, as an extreme case, you have just two unit cells (in each dimension) with 300A cell dimensions, the interference function could still manifest itself out to 1A resolution. Play around with some of James Holton's simulation programs to find out or use one of the Fresnel/Fraunhofer diffraction applets such as in http://www.falstad.com/diffraction/).
The reasons spots merge and become no longer measurable are due to factors like spread of cell dimensions, "mosaicity" or wavelength spread.
----------
From: Ed Pozharski
I apologize if I misled anyone. Re-reading my post, I can see that it
lacked precision. Indeed, in a perfect monocrystal all the molecules
are lined up perfectly, so I should have emphasized rather that the
culprit is the decay of correlation between atomic positions. It is
still a bit counterintuitive that a crystal can diffract beyond the
resolution seemingly allowed by possible bragg planes. Shouldn't the
"crystal size" formfactor introduce something akin to sinx/x that will
drive intensity rapidly down past the "bragg limit"? Oh well.
On a second thought, maybe the unit cell size does not matter directly.
What matters perhaps is how quickly the disorder accumulates over
distance, and that should be more pronounced for larger molecules. Thus
the problem is that larger molecules cannot pack as well as, say,
crambin.
On empirical side, the largest molecule currently in the PDB with d<1A
is 3ju4, 0.98A and ~75kDa.
See the distribution of sizes of "subangstrom" structures here.
http://tinyurl.com/8yhbcvk
BTW, the 3ju4 is reported on EDS as "unreliable". Shall comment in the
other thread.
----------
From: Jacob Keller
I think once you start getting down to such small crystals, the spots
are not really important, as the pattern starts getting continuous.
Interestingly enough, I guess for single-molecule diffraction,
resolution is limited only by radiation damage, and not by any sort of
lattice disorder (or even by its disorder wrt itself over time, seeing
as these images are collected in the fs range!) Each would seem to be
a perfect, unlimited-resolution fourier transform of that particular
molecule at that particular moment, and the resolution limits come
only when trying to merge the images/particles. It seems, then, that
if one somehow picked the images that were taken from the most similar
molecules, one could get better and better models...
JPK
----------
From: Colin Nave
Ed
The crystal size form factor will change the intensity of each spot so that instead of being a sharp maximum it will have a sinx/x behaviour. This will occur for each spot independently of resolution. There is a very good illustration of this in the paper referred to by Ethan where the sin(x)/x type fringes join up the spots so one can count the number of unit cells.
One doesn't see this normally because either one has lots of blocks of different sizes or, if there is just one block, the coherent length of the incident beam is smaller than the block size. Even if one satisfied the coherence condition, a very high resolution detector would be required (matched to the necessary beam divergence) for a normal size crystal.
I had a paper in 1999 describing some of these effects. I used the term sinc(x) as an alternative to sin(x)/x. This got changed to sine in the editing process but wasn't visible on the low resolution fax used to send the proofs (the old days!). I couldn't be bothered to produce a correction but have been waiting for 13 years for someone to point out this error. A small prize was waiting but it is too late now.
Of relevance to the initial question, one has to distinguish between short range and long range disorder. It is true that larger molecules will not pack as well as Crambin. There was some discussion of this at the CCP4 study weekend with issues such as the number of contacts between protein molecules as a function of their surface area. However, if the larger molecules maintain order over several unit cells, diffraction spots will still occur to high resolution. The reason that crystals of these larger molecules generally don't diffract to high resolution could be due to
1. The lack of contact between molecules and the larger solvent volumes mean that both the solvent and the protein (perhaps affected by the disordered solvent) will have short range disorder (i.e. not correlated between unit cells). This will lead to increased B factors.
2. Fewer strong contacts will lead to a variety of effects such as variation in unit cell size, smaller number of unit cells per block or angular variation between blocks. This longer range disorder will lead to increased spot sizes so that the spot eventually disappears below the background. James Holton has demonstrated that the background is the limiting factor for high resolution data collection.
3. The structure factors are lower for large unit cells. This will mean they will be harder to detect, particularly if there is a high background.
Well at least at the end there were some attempted answers to the original post.
Cheers
Colin
----------
From: Theresa H. Hsu
Thank you for the interesting replies so far.
Please let me ask a related question - at what resolution should we stop efforts to get better diffracting crystals? Are there *biological* questions that a model with 1.8-2.0 A resolution (with combination of complementary methods like spectroscopy) cannot answer than a model with < 1 A?
Theresa
----------
From: Ed Pozharski
Most of the time one does not need ultrahigh resolution to answer a
"biological question". Some examples of the opposite:
1. Anisotropic B-factors may provide some insight regarding
directionality of the protein dynamics
2. Unrestrained refinement at ultrahigh resolution allows to delineate
protonation states (e.g. by looking at the covalent bonds, sometimes you
can convince yourself that the density corresponding to the hydrogen is
actually present)
3. Alternate conformations may be clarified.
4. Improved precision allows to correlate changes in hydrogen/metal
bonds to enzymatic activity.
What, in broad terms, is your "biological question"? Knowing that would
allow for a more specific answer.
Cheers,
Ed.
--
"Hurry up before we all come back to our senses!"
Julian, King of Lemurs
----------
From: Pavel Afonine
One more to add to Ed's list:
highly accurate ultra-high resolution structures may allow calculation of electrostatic potential around protein ligand binding site. There are plenty of reference...
Pavel
----------
From: Artem Evdokimov
There are two sides to this qustion: the scientific one is actually easier to answer in generic terms - but I also would like to point out the very recent example of a mystery that required very high resoluton (and orthogonal techniques) to answer, namely the puzzle of the light atom in the center of the mofe nitrogenase protein. Highly recommended reading. At any rate the second side of this question is the logistics and cost\benefit ratio of pursuing ever higher resoluton. In most 'relatively simple' cases a solid 3A structure goes a long way towards answering a biological question, provided that additional techniques generate complmentary data. With the progress made in the area of modeling and simulation the value of mid-res structures grows since they now may be used as high quality restraints for modeling. So in each individual case we have to evaluate the particulars.... and if we choose not to pursue higher resolution, we must accept the associated risks and move on :-)
Artem
----------
From: Dirk Kostrewa
Dear Colin,
Am 10.01.12 18:08, schrieb Colin Nave:
<snip> </snip>
But aren't the total structure factors of a unit cell the sum of the atomic structure factors? For a larger unit cell (assuming a similar solvent content), I would then expect larger structure factors.
Best regards,
Dirk.
----------
From: Thomas Womack
That does sound interesting: could you give a reference? I can find various papers about small slices of the puzzle, but not a review article.
Tom
----------
From: Thomas Womack
http://www.sciencemag.org/content/334/6058/974.full is the work using orthogonal techniques to figure out which the light atom actually was, with a discussion at
The high-resolution structure that revealed that there was a light atom there is from 2002: http://www.sciencemag.org/content/297/5587/1696.full with discussion at http://www.sciencemag.org/content/297/5587/1654.full
Tom
----------
From: Colin Nave
Dirk
Yes. Equating the square root of the measured intensity (photons/spot) to the structure factor was sloppy nomenclature on my part.
One should look at Darwin's formula for the intensity (photons/spot). The adverse term in it is Vxtal/Vcell (ratio between crystal and cell volumes).
Regarding the scaling behaviour of the structure factors with respect to Vcell, I think section 2.7 of the Holton and Frankel article gives good explanations (i.e. looking at the issue from more than one point of view). See
The minimum crystal size needed for a complete diffraction data set, Acta Cryst. D, 66, 393-408 (2010).
http://journals.iucr.org/d/issues/2010/04/00/ba5148/ .
In short, the scaling of the (squared) structure factors compensates for the other Vcell term in the Darwin formula leaving one with the remaining adverse Vxtal/Vcell. For the same size crystal doubling each cell edge leads to average spot intensities being reduced by a factor of 8.
Thanks!
Colin
No comments:
Post a Comment