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
