The journal was Molecular Physics (1987) Vol 62(2), 451-459.
(my brain librates when I type)
Daniel Anderson wrote:
Maybe you should look at: "Rotation barriers in crystals from atomic
displacement parameters" Emily Maverick and Jack Dunitz (1987) Vol
62(2), 451-459.
They reported that the libration amplitude of one part of a
crystalline small molecule relative to another part is strongly
correlated to bond rotation barriers measured by other means. The
discussion at the top of page 458 seems to be about off rates. It's
not up to me if a multi-temperature diffraction experiment and a lot
of TLS analyses will be worth the effort relative to purchasing
equipment to measure a binding parameter.
-Dan
James Holton wrote:
I don't think there is any relationship between rate constants and B
factors. Yes, there is the hand-wavy argument of "disorder begets
disorder" (and people almost always LITERALLY wave their hands when
they propose this), but you have to be much more careful than that
when it comes to thermodynamics. Yes, "disorder" and entropy are
related, but just because a ligand is "disordered" does not mean that
the delta-S term of the binding delta-G is higher.
Now, there is a relationship between equilibrium constants and
occupancies, since the occupancy is really just the ratio of the
concentration of "protein-bound-to-ligand" to the total protein
concentration, and an equilibrium exists between these two species.
NB all the usual caveats of how crystal packing could change binding
constants, etc. You could logically extend this to B factors by
invoking a property of refinement: Specifically, if the "true"
occupancy is less than 1, but modeled as "1.00", your refinement
program will give you a B factor that is larger than the "true"
atomic B factor. However, if you try to make this claim, then the
obvious cantankerous reviewer suggestion would be to refine the
occupancy. Problem is, refining both occupancy and B at the same
time is usually unstable at moderate resolution. In general, it is
hard to distinguish between something that is flopping around (high B
factor) and something that is simply "not there" part of the time
(low occupancy).
I know it is tempting to try and relate B factors directly to
entropy, but the "disorder" that leads to large B factors has a lot
more to do with crystals than it has to do with proteins. For
example, there are plenty of tightly-bound complexes that don't
diffract well at all. If you refine these structures, you will get
big B factors (roughly, B = 4*d^2+12 where d is the resolution in
Angstrom). You may even have several crystal forms of the same thing
with different Wilson B factors, but that is in no way evidence that
the proteins in the two crystal forms somehow have different binding
constants or rate constants.
On the bright side, in your case it sounds like you have an entire
protomer that is "disorered" relative to the rest of the crystal
lattice. We have seen a few cases now like this where dehydrating
the crystal (with an FMS or similar procedure) causes the unit cell
to shrink and this "locks" the wobbly molecule into place. I think
this is the principle mechanism of "improved diffraction from
dehydration". No, it does not work very often! But sometimes it does.
-James Holton
MAD Scientist
On 11/19/2010 4:58 AM, Sebastiano Pasqualato wrote:
Hi all,
I have a crystallographical/biochemical problem, and maybe some of
you guys can help me out.
We have recently crystallized a protein:protein complex, whose Kd
has been measured being ca. 10 uM (both by fluorescence polarization
and surface plasmon resonance).
Despite the 'decent' affinity, we couldn't purify an homogeneous
complex in size exclusion chromatography, even mixing the protein at
concentrations up to 80-100 uM each.
We explained this behavior by assuming that extremely high Kon/Koff
values combine to give this 10 uM affinity, and the high Koff value
would account for the dissociation going on during size exclusion
chromatography. We have partial evidence for this from the SPR
curves, although we haven't actually measured the Kon/Koff values.
We eventually managed to solve the crystal structure of the complex
by mixing the two proteins (we had to add an excess of one of them
to get good diffraction data).
Once solved the structure (which makes perfect biological sense and
has been validated), we get mean B factors for one of the component
(the larger) much lower than those of the other component (the
smaller one, which we had in excess). We're talking about 48 Å^2 vs.
75 Å^2.
I was wondering if anybody has had some similar cases, or has any
hint on the possible relationship it might (or might not) exist
between high a Koff value and high B factors (a relationship we are
tempted to draw).
Thanks in advance,
best regards,
ciao
s
