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Jacob, In the formula: Kd=[P][L]/[PL] [P] and [L] are concentrations of UNBOUND protein and ligand, and [PL] is that in the complex. Since the occupancy of the ligand in the crystal is [ PL]/[Po]= 1/(Kd/L+1), varying [L] around Kd like from 0.1Kd to 10Kd will make the titration of occupancy. You can calculate from the provided formula which [L] will give 0.25, 0.5 and 0.75 occupancies. Forget that the protein is crystallized. We assume that its behavior has not changed due to it. In reality, ligand affinity of conformationally flexible proteins can change by many orders of magnitude in both directions. This is why soaking does not work sometimes and you have to do co-crystallization. If you decide to titrate a crystal with a ligand, you should collect data and refine the ligandless and fully-ocupied crystals first, then use the superimposition of their structures for refinement of all other cases. Take care of waters that substitute for the partially bound ligand, they should have occupancies =1-Occ_of_ligand. Good luck. Alex On Jun 27, 2011, at 10:04 AM, Jacob Keller wrote: > Yes, I think you are right--the somewhat counterintuitive case I was > thinking of was, for example, when: > > Kd = 20nM > [L] = 20uM > [Po in crystal] = 20mM > > In this case, even though [L] = 20uM, since [L] is 1000 x Kd, the > occupancy should be ~100%, and [PL] at equilibrium should be about > 20mM, so in the crystal, the total [L] should be ~20mM. This explains, > among other things, why bromophenol blue makes crystals bluer than the > surrounding solution--the Kd is probably significantly lower than the > BB concentration in the drop. > > Thanks for your clarifications! > > Jacob > > The question would remain, then, whether there is any utility in > titrating ligands into crystals, and monitoring occupancies as a > readout for binding. Although crystallization conditions are horribly > non-physiological, perhaps there would be utility in the case where > there are multiple known binding sites of various affinities, and > other methods would have trouble resolving the binding events. One > could start with: > > 1. totally saturated conditions, set occ=1 for all sites, refine B's, then > 2. fix B's at this value, and refine the occ's in a subsequent series > of dilutions. > > All of this is not totally theoretical--I am considering a set of > experiments along these lines, where there really are multiple sites > of varying affinity. > > ******************************************* > Jacob Pearson Keller > Northwestern University > Medical Scientist Training Program > cel: 773.608.9185 > email: [log in to unmask] > *******************************************