Re: [ccp4bb] Kd's in Crystals
Determination of Kd in crystal using only crystallographic data look at The First Direct Determination of a Ligand Binding Constant in Protein Crystals Wu SY, Dornan J., Kontopidis G., Taylor P., Walkinshaw M.D. Angew Chem Int Ed Engl, 2001, 40, 582-586. George --- George Kontopidis Associate Professor of Biochemistry Head of Biochemistry Veterinary School, University of Thessaly Trikalon 224, Karditsa 43100, Greece Tel: +30 24410 66017 Mob: 69 342 643 75 Fax: +30 24410 66041 e-mail: gkontopi...@vet.uth.gr web site: http://www.vet.uth.gr/english/departments_biochemistry.html --- -Original Message- From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of Steven Herron Sent: Monday, June 27, 2011 9:33 PM To: CCP4BB@JISCMAIL.AC.UK Subject: Re: [ccp4bb] Kd's in Crystals I had success using crystallography to measure the Ca2+ affinity (in the mM range) for a Ca2+ dependent enzyme. See: Characterization and implications of Ca2+ binding to pectate lyase C. Herron SR, Scavetta RD, Garrett M, Legner M, Jurnak F. J Biol Chem. 2003 Apr 4;278(14):12271-7. We measured the occupancy of the Ca2+ ion using three different pH's and 3-4 different Ca2+ concentrations. The presence of the Ca2+ ion altered the conformation of two residues in the binding pocket. In several of the Ca2+ soak experiment the occupancy was between 35% and 70%, where both orientations of the side chains could be modeled separately and their occupancy values refined (see attached picture). We confirmed our crystallographic Kd approach using tryptophan fluorescence. Since it was difficult to measure mM binding affinities using dialysis or titration calorimetry, we turned to crystallography (since we had lots of crystals and beam time). Steve Jacob Keller wrote: >Dear Crystallographers, > >what is the dogma with regard to affinities in crystals? For example, >if I soak three crystals in 1pM, 1nM, and 1uM compound X, and they all >show equivalent density, does that mean that the affinity is really >better than 1pM, or is the crystal of such a high local concentration >(~600mg/mL) that it will be fully occupied at nearly any concentration, >provided external ligand concentration does not change due to binding >in the crystal? I guess there is also the problem that the >crystallization solutions are very non-physiological, but neglecting >that, is there any straightforward way to think of this, or is there a >good reference? > >Jacob Keller > > >
Re: [ccp4bb] Kd's in Crystals
Hi, You may want to have a look at the two papers below. Experimental determination of van der waals energies in a biological system. Wear MA, Kan D, Rabu A, Walkinshaw MD. Angew Chem Int Ed Engl. 2007;46(34):6453-6. The First Direct Determination of a Ligand Binding Constant in Protein Crystals. Wu Sy S, Dornan J, Kontopidis G, Taylor P, Walkinshaw MD. Angew Chem Int Ed Engl. 2001 Feb 2;40(3):582-586. Regards Iain Quoting Jacob Keller on Mon, 27 Jun 2011 12:04:35 -0500: 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: j-kell...@northwestern.edu *** Dr. Iain McNae School of Biological Sciences Institute of Structural and Molecular Biology The University of Edinburgh Kings Building?s Mayfield Road Edinburgh EH9 3JR Fax 0131 650 7055 Telephone 0131 650 7052 Mobile 07969 304 852 -- The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336.
Re: [ccp4bb] Kd's in Crystals
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: j-kell...@northwestern.edu > ***
Re: [ccp4bb] Kd's in Crystals
Hi, We had a paper where we looked at Kd of arginine in the arginine repressor-DNA complex (p. 248-249). JMB,2010, *399*, pp.240-254. Maia 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: j-kell...@northwestern.edu ***
Re: [ccp4bb] Kd's in Crystals
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: j-kell...@northwestern.edu ***
Re: [ccp4bb] Kd's in Crystals
Jacob, In case if the hint that I sent yesterday was not clear, below is the solution for the equation Kd=[P][L]/[PL] in terms of ligand occupancy: O=[ PL]/[Po]= 1/(Kd/L+1) You see, it does not depend on [Po] Alex On Jun 26, 2011, at 10:05 AM, aaleshin wrote: > The concentration of a protein in a crystal [Po] and the volume of a crystal > V are needed only to calculate the total amount of a ligand [Lo] required for > soaking. > [Lo] > [Po]*V > > The occupancy of the active sites in a crystal will depend only on the ligand > concentration in solution and Kd. It does not depend on protein concentration > in the crystal. > > Indeed: > Kd=[P][L]/[PL] > > Assuming total concentration of the protein = Po, Kd= 1mM and S= 1 mM, the > active site occupancy will be: > > 1= P/Po-P; > > P/Po=1/2 > > So the concentration of the ligand in solution should be >>Kd to get the full > occupancy. > > Alex >
Re: [ccp4bb] Kd's in Crystals
The concentration of a protein in a crystal [Po] and the volume of a crystal V are needed only to calculate the total amount of a ligand [Lo] required for soaking. [Lo] > [Po]*V The occupancy of the active sites in a crystal will depend only on the ligand concentration in solution and Kd. It does not depend on protein concentration in the crystal. Indeed: Kd=[P][L] / [PL] (chemical equilibrium equation) Assuming total concentration of the protein = Po, Kd= 1mM and S= 1 mM, the active site occupancy will be: 1= P/Po-P; P/Po=1/2 So the concentration of the ligand in solution should be >>Kd to get the full occupancy. Alex On Jun 25, 2011, at 9:19 PM, Jacob Keller wrote: > Upon some reflection, I think one can say this: first, let's say the > protein in question is 30kD, with a solvent content of 50%, and we > know that solid protein density is ~1200mg/mL. Therefore, the protein > concentration in the crystal would be ~20mM. Because Kd's assume > infinitesimal ligand concentration, I think that neglecting ligand > depletion effects mentioned by Edward Berry, say by having a huge > reservoir or transferring the crystal to an appropriate soaking > environment, that all ligands which bind with a better than ~20mM Kd > should be bound in that crystal, even at extremely low ligand > concentrations, so changing [ligand] from 1pM to 10mM should not > change occupancy much, again assuming equilibrium and neglecting > ligand depletion. > > JPK
Re: [ccp4bb] Kd's in Crystals
Upon some reflection, I think one can say this: first, let's say the protein in question is 30kD, with a solvent content of 50%, and we know that solid protein density is ~1200mg/mL. Therefore, the protein concentration in the crystal would be ~20mM. Because Kd's assume infinitesimal ligand concentration, I think that neglecting ligand depletion effects mentioned by Edward Berry, say by having a huge reservoir or transferring the crystal to an appropriate soaking environment, that all ligands which bind with a better than ~20mM Kd should be bound in that crystal, even at extremely low ligand concentrations, so changing [ligand] from 1pM to 10mM should not change occupancy much, again assuming equilibrium and neglecting ligand depletion. JPK
Re: [ccp4bb] Kd's in Crystals
Hi, I think inside a protein crystal, it is a macromolecular crowding environment. According to what I read, it seems that in a crowding environment, the KD of proteins to ligands may change - often gets tighter. As we know, 20-80% of the total volume in a protein crystal is occupied by the protein molecules, which leaves less volume for the solvent. Also instead of having all directions to diffuse, a small molecule's movement in a protein crystal's solvent channel is restricted by the geometry of the channel: the protein molecules form a static mesh, and the ligands cannot penetrate the protein molecules. I suspect that under such conditions some of the presumptions upon which the KD is defined would not hold true. As I understand, essentially the KD definition is a probabilistic collision model of tiny, spherical, free moving points in a continuous space with dimensions considerably larger than that of the reactants. If the volume for the molecules to move around is reduced and the movements are also restricted by geometric factors, I would imagine that more collision will occur thus more binding will take place. Zhijie -- From: "Jacob Keller" Sent: Friday, June 24, 2011 6:58 PM To: Subject: [ccp4bb] Kd's in Crystals Dear Crystallographers, what is the dogma with regard to affinities in crystals? For example, if I soak three crystals in 1pM, 1nM, and 1uM compound X, and they all show equivalent density, does that mean that the affinity is really better than 1pM, or is the crystal of such a high local concentration (~600mg/mL) that it will be fully occupied at nearly any concentration, provided external ligand concentration does not change due to binding in the crystal? I guess there is also the problem that the crystallization solutions are very non-physiological, but neglecting that, is there any straightforward way to think of this, or is there a good reference? Jacob Keller -- *** Jacob Pearson Keller Northwestern University Medical Scientist Training Program cel: 773.608.9185 email: j-kell...@northwestern.edu ***
Re: [ccp4bb] Kd's in Crystals
Jacob Keller wrote: Dear Crystallographers, what is the dogma with regard to affinities in crystals? For example, if I soak three crystals in 1pM, 1nM, and 1uM compound X, and they all show equivalent density, does that mean that the affinity is really better than 1pM, or is the crystal of such a high local concentration (~600mg/mL) that it will be fully occupied at nearly any concentration, provided external ligand concentration does not change due to binding in the crystal? I guess there is also the problem that the crystallization solutions are very non-physiological, but neglecting that, is there any straightforward way to think of this, or is there a good reference? Is it a hypothetical question, or experimental result? From a simplistic viewpoint, concentration of the protein does not affect the Kd, i.e. the concentration of free ligand at which the sites are half occupied. All the usual equations work, but you have to remember that [Ligand] refers to concentration of _free_ ligand, and since the protein concentration is so high (100 uM to 1 mM say) in the drop, that free ligand is likely to be a small fraction of total. Thus if you add 1 pM ligand to the drop, you will not get significant binding even with infinitely high affinity. If you dialyze your crystal against liters and liters of 1 pM ligand solution, you might get high occupancy, and that would indeed mean the Kd is < 1 pM, but i don't think that is very practical. Basically you need to add equimolar ligand plus an additional concentration say 10 x the Kd to satisfy the Maybe if you soak a single tiny crystal in a reasonalble volume of buffer at 1 pM, it would be enough? say (0.1 mm)^3 crystal containing 1 mM biding sites (which corresponds to a rather large ASU, most crystals would be higher) you would need 10^6 times the volume or 1 ml of 1 pM solution to have one ligand for every site. But then the free ligand concentration would be zero. Jacob Keller -- *** Jacob Pearson Keller Northwestern University Medical Scientist Training Program cel: 773.608.9185 email: j-kell...@northwestern.edu ***
[ccp4bb] Kd's in Crystals
Dear Crystallographers, what is the dogma with regard to affinities in crystals? For example, if I soak three crystals in 1pM, 1nM, and 1uM compound X, and they all show equivalent density, does that mean that the affinity is really better than 1pM, or is the crystal of such a high local concentration (~600mg/mL) that it will be fully occupied at nearly any concentration, provided external ligand concentration does not change due to binding in the crystal? I guess there is also the problem that the crystallization solutions are very non-physiological, but neglecting that, is there any straightforward way to think of this, or is there a good reference? Jacob Keller -- *** Jacob Pearson Keller Northwestern University Medical Scientist Training Program cel: 773.608.9185 email: j-kell...@northwestern.edu ***
