Ahh yes. I still have the very helpful email I got from Dame Louise
Johnson in 2010. I don't think she would mind my quoting it here:
Dear James
I was sorry to miss you when you were at Diamond - I was in Germany.
The story of the two forms of lysozyme crystals goes back to about 1964 when
it was found that the diffraction patterns from different crystals could be
placed in one of two classes depending on their intensities. This discovery
was a big set back at the time and I can remember a lecture title being
changed from the 'The structure of lysozyme' to 'The structure of lysozyme
two steps forward and one step back'. Thereafter the crystals were
screened based on intensities of the (11,11,l) rows to distinguish them
(e.g. 11,11,4 > 11,11,5 in one form and vice versa in another). Data were
collected only for those that fulfilled the Type II criteria. (These
reflections were easy to measure on the linear diffractometer because
crystals were mounted to rotate about the diagonal axis). As I recall both
Type I and Type II could be found in the same crystallisation batch .
Although sometimes the external morphology allowed recognition this was not
infallible.
The structure was based on Type II crystals. Later a graduate student Helen
Handoll examined Type I. The work, which was in the early days and before
refinement programmes, seemed to suggest that the differences lay in the
arrangement of water or chloride molecules (Lysozyme was crystallised from
NaCl). But the work was never written up. Keith Wilson at one stage was
following this up as lysozyme was being used to test data collection
strategies but I do not know the outcome.
An account of this is given in International Table Volume F (Rossmann and
Arnold edited 2001) p760.
Tony North was much involved in sorting this out and if you wanted more info
he would be the person to contact.
I hope this is helpful. Do let me know if you need more.
Best wishes
Louise
Armed with this advice, I searched the PDB using what I call the
"Johnson ratio" of F(11,11,4) / F(11,11,5) and found there was a
continuous spectrum (pasted below). The extrema of this spectrum were
3aw6 and 3aw7 (circled), which are not only from the same paper, but
from the same crystal: a dehydration study. Despite a modest unit cell
size change of 0.7%, the R-factor between the Fobs of these two entries
(aka R-iso) is 44%. Its like they are different proteins, and a 12%
change in relative humidity was all it took. I never did get a chance
to tell Louise that it was a dehydration effect. It took me too long to
figure it out. But, I expect she would have found that information
delightful.
To weigh in on the OP:
First: @Doeke, no I am not reviewing your new paper, but I hope whomever
is is being helpful.
Second: I am with Randy Read that isomorphism means "same shape", and
also with Bernhard Rupp that "same" is resolution dependent. Anything is
"isomorphous" if you stand far enough away from it (like Carl Sagan's
"pale blue dot"). So, I personally define "isomorphism" in terms of the
agreement between the structure factors (Fobs). When does it become
non-isomorphism? I say this is when the changes in Fobs become
intolerable. What is intolerable? Depends on what you are doing, but in
general it is good to compare the effect of interest to the existing
noise. If the changes in Fobs due to the structural shift become larger
than SIGFobs, then you start having "non-isomorphism". For the common
example of merging data from multiple crystals, non-isomorphism becomes
intolerable when it is large enough to degrade rather than improve your
signal-to-noise after merging.
For comparing maps, I'd say non-isomorphism becomes intolerable when the
difference peaks due to uninteresting movements becomes larger than
those due to interesting changes. What is interesting? Depends on what
is causing it. Large-scale domain motions due to laser-induced heat are
perhaps "not interesting" (to some), but large-scale domain motions due
to allosteric regulation are "interesting" (to some). Other
"interesting" things like ligand binding are an occupancy shift, which
are traditionally not considered non-isomorphism because the xyz
positions aren't changing (recall the definition of "isomorphous
replacement"). The term "non-isomorphism" is usually used to describe a
large-scale positional shift.
These large-scale shifts are perhaps why changes in the unit cell can
be an indicator of isomorphism, but in my experience this relationship
is weak. This is especially true with serial crystallography where all
three cell dimensions are seldom constrained by a single image. That is,
there are sources of error that affect the accuracy of spot positions
(measured cell), but not the intensities (structure factors). So, my
advice is to take cell-based metrics of "isomorphism" with a grain of salt.
It has already been pointed out that a pure scaling cell deformation
(one that preserves all the fractional coordinates of all the atoms)
does not change the structure factors. I would call such a pair of
crystals isomorphous.
The origin of the cell-based rule of thumb quoted in Drenth is indeed
the 1956 paper by Crick and Magdoff that John Cooper shared. But I must
stress: their calculation, while groundbreaking, was incredibly
simplistic. It was equivalent to changing the header of a PDB file to a
different unit cell, leaving all the atoms at the same orthogonal x,y,z
positions without regard for crystal packing and non-bond clashes. The
non-physical-ness of this approach is perhaps why noone has ever
re-visited it. It is also maximally pessimistic, as real crystals are
no doubt somewhere in between the harshly rigid approximation of Crick &
Magdoff and the perfectly soft elasticity that yields no change in
structure factors at all.
To be fair, I suspect the computer used to do these calculations was
named Beatrice Magdoff. That is, in 1956 a "computer" was a job
description, not a device. Magdoff did some amazing things in her
career, and this one was no doubt a lot of work. I don't blame her and
Crick for trying to keep it simple. I would have done the same. I also
suspect Magdoff would agree that computers in 2024 are a bit more
powerful than the fastest computers of 1956.
I expect in the coming year that barriers like non-isomorphism will
start to be overcome. No doubt borrowing from our cryo-EM friends who
have been stretching, pulling and sharpening 3D images for decades.
Happy New Year everyone!
-James Holton
MAD Scientist
On 12/21/2023 11:37 AM, Tom Peat wrote:
Hello All,
I think Randy makes a very good point here- it depends on what you are
trying to do with your data sets.
If you are trying to merge them, 'isomorphous' is important for this
to work. If you are using them for cross crystal averaging, being less
isomorphous is better (more signal).
James Holton has a story of Louise Johnson collecting data on lysozyme
(back in the 60's?) where she looked at one specific reflection to
determine whether the data sets she was collecting would be
isomorphous and scale. It turns out that although the cell was very
similar, the dehydration state of the crystal was very important for
two lysozyme data sets to scale together. The Rmerge for the two
dehydration states was something crazy large, like 44%, even though
under the standard 'rules' (more rules of thumb), one would have
believed that these data sets should have been 'isomorphous'. For the
data sets that had the same dehydration state, the data merged with
'typical' statistics of lysozyme (like 3-4%).
James will have the details that I do not.
cheers, tom
------------------------------------------------------------------------
*From:* CCP4 bulletin board <CCP4BB@JISCMAIL.AC.UK> on behalf of Randy
John Read <rj...@cam.ac.uk>
*Sent:* Thursday, December 21, 2023 10:53 PM
*To:* CCP4BB@JISCMAIL.AC.UK <CCP4BB@JISCMAIL.AC.UK>
*Subject:* Re: [ccp4bb] what is isomorphous?
[You don't often get email from rj...@cam.ac.uk. Learn why this is
important at https://aka.ms/LearnAboutSenderIdentification ]
I think we’ve strayed a bit from Doeke’s original question involving
crystals A, B and C, where I think the consensus opinion would be that
we would refer to crystal C as not being isomorphous to either A or B.
On the question of what “isomorphous” means in the context of related
crystals, I’m not sure we have complete consensus. I would tend to say
that any two crystals are isomorphous if they have related unit cells
and similar fractional coordinates of the atoms, so that
(operationally) their diffraction patterns are correlated. However,
there might be differences of opinion on whether two crystals can be
considered isomorphous if one has exact crystallographic symmetry and
the other has pseudosymmetry. (I would probably be on the more
permissive side here.)
In principle, I suppose being isomorphous (“same shape”) should be a
binary decision, but in practice we’re interested in the implications
of the degree to which perfect isomorphism is violated. So I would
tend to use the term “poorly isomorphous” for a pair where the
correlation between the diffraction patterns drops off well before the
resolution limit. Crick was focused on percentage change in cell
dimensions, but Bernhard is right that what matters is the ratio
between the difference in cell lengths and the resolution of the data.
It’s a bit counter-intuitive, but the effect of the difference between
cell edges of 20 and 25 is the same as for cell edges of 200 and 205!
By the way, the first time I learned this was from K. Cowtan and I
hadn’t realised it’s also in Jan Drenth’s book.
For isomorphous replacement (something some of us dimly remember from
the days before AlphaFold), being poorly isomorphous is bad, but for
cross-crystal averaging the more poorly isomorphous the better,
because the molecular transform is being sampled in different places
in reciprocal space.
Best wishes,
Randy Read
> On 21 Dec 2023, at 10:53, Jon Cooper
<0000488a26d62010-dmarc-requ...@jiscmail.ac.uk> wrote:
>
> Hello Harry,
>
> I think this is the paper you mean:
> https://scripts.iucr.org/cgi-bin/paper?S0365110X56002552
>
> They gave depressingly low estimates of how much the cell dimensions
could change in order for isomorphous replacement to still work. In
reality, unit cells can shrink and swell, but the fractional atomic
coordinates remain relatively unchanged (right?) so bigger unit cell
differences still allow the method to work.
>
> Best wishes, Jon Cooper. jon.b.coo...@protonmail.com
>
> Sent from Proton Mail mobile
>
>
>
> -------- Original Message --------
> On 21 Dec 2023, 09:07, Harry Powell <
0000193323b1e616-dmarc-requ...@jiscmail.ac.uk> wrote:
> Hi Didn’t Francis Crick have something to say about this in the
early 1950s? I’m sure it was published but off the top of my mind I
can’t think where (one of the more “established” members of this
community will be able to give chapter and verse)! If you want to read
something a little more detailed than people have mentioned here,
there’s a “Methods in Enzymology” chapter by Charlie Carter (?) et al
from the early part of this century on the subject - again, I can’t
remember exactly who or when. Have a good break (which reminds me to
register for the CCP4 Study Weekend)! Harry > On 21 Dec 2023, at
08:04, Tim Gruene wrote: > > Hi Doeke, > > you can take the
coordinates of B and do a rigid body refinement > against the data
from A. If this map is sufficient to reproduce model A > (including
model building and more refinement cycles), then B is > isomorphous to
A. You can do this the other way round, and the result > may not be
the same - hence, the mathematical definition of isomorphous > is not
identical to the practical use of 'isomorphous' structures when > it
comes to phasing. You can repeat this for each side of the triangle >
(each in two directions) in order to label the semantic triangle. > >
Merry Christmas, more peace on earth and sanity for the elections in >
2024! > > Tim > > On Wed, 20 Dec 2023 20:15:17 +0000 "Hekstra, Doeke
Romke" > wrote: > >> Dear colleagues, >> >> Something to muse over
during the holidays: >> >> Let's say we have three crystal forms of
the same protein, for >> example crystallized with different ligands.
Crystal forms A and B >> have the same crystal packing, except that
one unit cell dimension >> differs by, for example, 3%. Crystal form C
has a different crystal >> packing arrangement altogether. What is the
right nomenclature to >> describe the relationship between these
crystal forms? >> >> If A and B are sufficiently different that their
phases are >> essentially uncorrelated, what do we call them?
Near-isomorphous? >> Non-isomorphous? Do we need a different term to
distinguish them from >> C or do we call all three datasets
non-isomorphous? >> >> Thanks for helping us resolve our semantic
tangle. >> >> Happy holidays! >> Doeke >> >> ===== >> >> Doeke Hekstra
>> Assistant Professor of Molecular & Cellular Biology, and of Applied
>> Physics (SEAS), Director of Undergraduate Studies, Chemical and >>
Physical Biology Center for Systems Biology, Harvard University >> 52
Oxford Street, NW311 >> Cambridge, MA 02138 >> Office: 617-496-4740 >>
Admin: 617-495-5651 (Lin Song) >> >> >> >>
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Department of Haematology, University of Cambridge
Cambridge Institute for Medical Research Tel: +44 1223 336500
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