Although Bfactors and occupancies are correlated, occupancy refinement is quite feasible for the following reasons:
1) Modern maximum likelyhood programs like Buster do a decent job in separating occupancies and Bfactors. It shows up as shells of negative difference density e.g. around partially occupied metal ions which have been refined with full occupancy and inflated Bfactors. 2) A ligand is either completely there or it is completely gone, i.e. it is not that one could refine a group occupancy, one should refine a group occupancy and one has only one parameter to refine for say a ligand of 10+ atoms. In my experience, refining group occupancies even at moderate resolution, is stable. I now refine by default (group) occupancies for all ligands. These include the inhibitor soaked in, but also items like bound sulfate and phosphate ions, Tris, Hepes molecules and bound metal ions like zinc or cadmium. Only waters I refine at full occupancy and let the Bfactors soak up any partial occupancy and other errors since here the data do not allow occupancy refinement. Best, Herman -----Original Message----- From: CCP4 bulletin board [mailto:[email protected]] On Behalf Of James Holton Sent: Friday, November 19, 2010 9:20 PM To: [email protected] Subject: Re: [ccp4bb] relationship between B factors and Koff 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 > >
