Estimation of ligand binding affinity by occupancy refinement
Dear all, I have a question about sensitivity of occupancy refinement in phenix. I have a series of datasets done at our home instrument of relatively modest resolutions from 2.8 to 3 A. These are performed on crystals soaked in progressively higher ligand concentrations. We are trying to see to which of the several active sites the ligand binds first so we went from low to high ligand concentrations. We wanted to estimate the amount of ligand bound by refining the occupancies of the ligand. We expect one active site to bind more strongly than the other two active sites. This was indeed what we observed but when we refine the occupancies of the ligands in weaker binding sites starting at 0.2 occupancies they rise to 0.5-0.6 although some atoms are totally out of density and some are in. B factors are reasonable, i.e. don't go wild. My question would be: how reliable is this estimation of ligand binding by occupancy refinement? Why doesn't the occupancy of ligands stay low if afterwards the density fit of the ligand looks rather unconvincing? Thank you in advance Zoran -- Dr. Zoran Stefanic Division of Physical Chemistry Rudjer Boskovic Institute Bijenicka 54 P.O. Box 180 Zagreb Croatia Phone: 00 385 1 457 1203 Fax: 00 385 1 468 0245
Hi Zoran,
I have a question about sensitivity of occupancy refinement in phenix. I have a series of datasets done at our home instrument of relatively modest resolutions from 2.8 to 3 A.
occupancies and B-factors are correlated, especial at resolutions around 2.5A and lower; see for example: Correlation between occupancy and temperature factors of solvent molecules in crystal structures of proteins. T. Bhat, Acta Cryst. (1989). A45, 145-146.
These are performed on crystals soaked in progressively higher ligand concentrations. We are trying to see to which of the several active sites the ligand binds first so we went from low to high ligand concentrations. We wanted to estimate the amount of ligand bound by refining the occupancies of the ligand. We expect one active site to bind more strongly than the other two active sites. This was indeed what we observed but when we refine the occupancies of the ligands in weaker binding sites starting at 0.2 occupancies they rise to 0.5-0.6 although some atoms are totally out of density and some are in. B factors are reasonable, i.e. don't go wild.
"Totally out of density" is not a precise description. Which level you use to draw the 2mFo-DFc map? Did you look at 0.5 sigma (that's what I would use to look at weakly/partially occupied site)? What's the local map CC? What are the mFo-DFc (both, full and ligand-omit) and 2mFo-DFc map values at atomic centers of the ligand? phenix.model_vs_data used with comprehensive=true flag will give you all these values. Did you refine group occupancy of the ligand - that is one occupancy factor per whole ligand? What happens if you run say a few dozens refinements until full convergence (say 10-20 macro-cycles) each refinement starting with different initial value of ligand's occupancy and B-factor? Do all refinements arrive at the same refined occupancy and B? If not, the spread in refined values will give you the uncertainty.
My question would be: how reliable is this estimation of ligand binding by occupancy refinement?
The test suggested above will give you an idea about the answer. Pavel
Pavel's test of the robustness of the resulting occupancy with respect to its starting value provides only a lower bound for the uncertainty of that parameter. The goal of refinement is to find the most probable value for the set of parameters. If you imagine the probability distribution as a Gaussian, the ability to repeatedly determine the location of the peak of the distribution does not tell you much about its width. Compounding the problem is the correlation between the occupancies and B factors of the atoms. You can get very similar likelihoods when increasing both parameters, but if you hold one fixed and vary the other the likelihood changes very rapidly. On the other hand, I strongly suggest that you calculate the difference in Ki or the difference in binding energy between a ligand that binds with 0.1 occupancy and one that binds with 0.9. The entire range of occupancies distinguishable by x-ray crystallography cover only a small range of Ki. There is way less than one order of magnitude between the smallest occupancy indistinguishable from zero and the largest occupancy indistinguishable from one, and yet Ki's routinely vary by many orders of magnitude. Only by the most fantastic stroke of luck would the range of Ki for your inhibitors fall into the tiny range measurable by x-ray diffraction. Dale Tronrud On 04/27/12 10:01, Pavel Afonine wrote:
Hi Zoran,
I have a question about sensitivity of occupancy refinement in phenix. I have a series of datasets done at our home instrument of relatively modest resolutions from 2.8 to 3 A.
occupancies and B-factors are correlated, especial at resolutions around 2.5A and lower; see for example:
Correlation between occupancy and temperature factors of solvent molecules in crystal structures of proteins. T. Bhat, Acta Cryst. (1989). A45, 145-146.
These are performed on crystals soaked in progressively higher ligand concentrations. We are trying to see to which of the several active sites the ligand binds first so we went from low to high ligand concentrations. We wanted to estimate the amount of ligand bound by refining the occupancies of the ligand. We expect one active site to bind more strongly than the other two active sites. This was indeed what we observed but when we refine the occupancies of the ligands in weaker binding sites starting at 0.2 occupancies they rise to 0.5-0.6 although some atoms are totally out of density and some are in. B factors are reasonable, i.e. don't go wild.
"Totally out of density" is not a precise description. Which level you use to draw the 2mFo-DFc map? Did you look at 0.5 sigma (that's what I would use to look at weakly/partially occupied site)? What's the local map CC? What are the mFo-DFc (both, full and ligand-omit) and 2mFo-DFc map values at atomic centers of the ligand? phenix.model_vs_data used with comprehensive=true flag will give you all these values.
Did you refine group occupancy of the ligand - that is one occupancy factor per whole ligand?
What happens if you run say a few dozens refinements until full convergence (say 10-20 macro-cycles) each refinement starting with different initial value of ligand's occupancy and B-factor? Do all refinements arrive at the same refined occupancy and B? If not, the spread in refined values will give you the uncertainty.
My question would be: how reliable is this estimation of ligand binding by occupancy refinement?
The test suggested above will give you an idea about the answer.
Pavel
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one, and yet Ki's routinely vary by many orders of magnitude. Only by the most fantastic stroke of luck would the range of Ki for your inhibitors fall into the tiny range measurable by x-ray diffraction.
But by varying the ligand concentration over three orders of magnitude (uM to mM) you could improve the chances a bit? But since the protein itself is probably mM this would require protein and ligand concentration very accurately to estimate free concentration. And if the Kd is much below the protein concentration it will look like stoichiometric binding. Kind of the opposite of the dialysis method, where Kd needs to be below the protein concentration. So useful range would be from protein concentration up to the solubility of the ligand (or where it interferes with crystallization) which could be quite limited. I would not be so pessimistic about estimating occupancy, at least if the ligand is fairly large. The B factor spreads the density out, but integrated electron density over a largish area should be the same. For an individual atom the density might get lost by spreading out under other atoms, but for a cluster of atoms what is lost from one will mostly be gained by others, and in the end the refinement program has to account total electron density in the area. I remember one well-known crystallographer used a procedure of calibrating occupancy by integrating the electron density of a single well-defined water (perhaps in a difference map omitting the water). I once did Pavel's test by setting occupancy of a segment of the protein main chain to 0.5 or 2 and refining occupancy (as a single group). It returned pretty well to 1. in both cases. As already mentioned, if occupancy is partial you will need to contour at a lower level to get coverage. What about the difference maps? is there positive difference density if you refine with occupancy fixed at 0.2? Is there negative difference density if you allow it to refine to around 0.5? If yes and no, I would tend to trust the refinement. But try approaching the refined value from both sides as was suggested. eab Dale Tronrud wrote:
Pavel's test of the robustness of the resulting occupancy with respect to its starting value provides only a lower bound for the uncertainty of that parameter. The goal of refinement is to find the most probable value for the set of parameters. If you imagine the probability distribution as a Gaussian, the ability to repeatedly determine the location of the peak of the distribution does not tell you much about its width.
Compounding the problem is the correlation between the occupancies and B factors of the atoms. You can get very similar likelihoods when increasing both parameters, but if you hold one fixed and vary the other the likelihood changes very rapidly.
On the other hand, I strongly suggest that you calculate the difference in Ki or the difference in binding energy between a ligand that binds with 0.1 occupancy and one that binds with 0.9. The entire range of occupancies distinguishable by x-ray crystallography cover only a small range of Ki. There is way less than one order of magnitude between the smallest occupancy indistinguishable from zero and the largest occupancy indistinguishable from one, and yet Ki's routinely vary by many orders of magnitude. Only by the most fantastic stroke of luck would the range of Ki for your inhibitors fall into the tiny range measurable by x-ray diffraction.
Dale Tronrud
On 04/27/12 10:01, Pavel Afonine wrote:
Hi Zoran,
I have a question about sensitivity of occupancy refinement in phenix. I have a series of datasets done at our home instrument of relatively modest resolutions from 2.8 to 3 A.
occupancies and B-factors are correlated, especial at resolutions around 2.5A and lower; see for example:
Correlation between occupancy and temperature factors of solvent molecules in crystal structures of proteins. T. Bhat, Acta Cryst. (1989). A45, 145-146.
These are performed on crystals soaked in progressively higher ligand concentrations. We are trying to see to which of the several active sites the ligand binds first so we went from low to high ligand concentrations. We wanted to estimate the amount of ligand bound by refining the occupancies of the ligand. We expect one active site to bind more strongly than the other two active sites. This was indeed what we observed but when we refine the occupancies of the ligands in weaker binding sites starting at 0.2 occupancies they rise to 0.5-0.6 although some atoms are totally out of density and some are in. B factors are reasonable, i.e. don't go wild.
"Totally out of density" is not a precise description. Which level you use to draw the 2mFo-DFc map? Did you look at 0.5 sigma (that's what I would use to look at weakly/partially occupied site)? What's the local map CC? What are the mFo-DFc (both, full and ligand-omit) and 2mFo-DFc map values at atomic centers of the ligand? phenix.model_vs_data used with comprehensive=true flag will give you all these values.
Did you refine group occupancy of the ligand - that is one occupancy factor per whole ligand?
What happens if you run say a few dozens refinements until full convergence (say 10-20 macro-cycles) each refinement starting with different initial value of ligand's occupancy and B-factor? Do all refinements arrive at the same refined occupancy and B? If not, the spread in refined values will give you the uncertainty.
My question would be: how reliable is this estimation of ligand binding by occupancy refinement?
The test suggested above will give you an idea about the answer.
Pavel
_______________________________________________ phenixbb mailing list [email protected] http://phenix-online.org/mailman/listinfo/phenixbb
phenixbb mailing list [email protected] http://phenix-online.org/mailman/listinfo/phenixbb
I'm having a small problem with format - entering fixed_ensembles in automr: my input: fixed_ensembles { fixed_ensembleID_list = "ensemble_1" fixed_euler_list = 87.09 64.28 257.24 fixed_frac_list = 0.540 0.079 0.069 fixed_frac_list_is_fractional = True } Phenix output: Adding Ensemble ensemble_1 as fixed solution with: Euler angles: [87.09, 64.28, 257.24] Coords (orthogonal A): [0.54, 0.079, 0.069] *************ERROR ENDING ******************* **************************************** AutoMR Input failed Python argument types in SOLU.addSOLU_6DIM_ENSE(InputMR_AUTO, str, list, bool, list, float, bool, bool, bool) did not match C++ signature: addSOLU_6DIM_ENSE(phaser::SOLU {lvalue}, std::string, scitbx::vec3<double>, bool, scitbx::vec3<double>, double, bool, bool, bool, bool, scitbx::vec3<double>, double) **************************************** *************ERROR ENDING ******************* [1 In addition to fixed two solutions is it necessary to repeat the key phrases or can one add to "fixed_euler_list" in groups of three (do they need to be comma delimited? Nora Dr N B Cronin X-Ray Laboratory Manager Tel. (+44) 020 7153 5445 Section of Structural Biology Fax. (+44) 020 7153 5456 Chester Beatty Laboratories mobile: (+44) 07787554059 The Institute of Cancer Research 237 Fulham Road London SW3 6JB The Institute of Cancer Research: Royal Cancer Hospital, a charitable Company Limited by Guarantee, Registered in England under Company No. 534147 with its Registered Office at 123 Old Brompton Road, London SW7 3RP. This e-mail message is confidential and for use by the addressee only. If the message is received by anyone other than the addressee, please return the message to the sender by replying to it and then delete the message from your computer and network.
what does this have to do with estimating ligand binding affinity? Does one have to have fairly low occupancy? I have examples where one end of a ligand is much better defined than the other end of the ligand, both ends are in the same pocket. The pocket has to reshape to accomodate high affinity binding. We have modeled complete occupancy, but B factors for example would differ and we go from two conformations in rather diffuse density to excellent density at the one end of the pocket, while at the other end there is always excellent density. It seems magical to convert this type of data to affinity, but if there was a way, I would be interested in trying it. With my best regards, Tim Timothy A. Springer, Ph.D. Latham Family Professor of Biological Chemistry and Molecular Pharmacology Harvard Medical School http://idi.harvard.edu/springer Immune Disease Institute [email protected] Program in Cellular and Molecular Medicine, Dept. Medicine Div. Hematology Children's Hospital Boston 3 Blackfan Circle, Rm 3103 phone: 617-713-8200 Boston MA 02115 fax: 617-713-8232 On May 1, 2012, at 9:32 AM, Nora Cronin wrote:
I'm having a small problem with format - entering fixed_ensembles in automr:
my input:
fixed_ensembles { fixed_ensembleID_list = "ensemble_1" fixed_euler_list = 87.09 64.28 257.24 fixed_frac_list = 0.540 0.079 0.069 fixed_frac_list_is_fractional = True }
Phenix output:
Adding Ensemble ensemble_1 as fixed solution with: Euler angles: [87.09, 64.28, 257.24] Coords (orthogonal A): [0.54, 0.079, 0.069] *************ERROR ENDING *******************
**************************************** AutoMR Input failed Python argument types in SOLU.addSOLU_6DIM_ENSE(InputMR_AUTO, str, list, bool, list, float, bool, bool, bool) did not match C++ signature: addSOLU_6DIM_ENSE(phaser::SOLU {lvalue}, std::string, scitbx::vec3<double>, bool, scitbx::vec3<double>, double, bool, bool, bool, bool, scitbx::vec3<double>, double) **************************************** *************ERROR ENDING ******************* [1
In addition to fixed two solutions is it necessary to repeat the key phrases or can one add to "fixed_euler_list" in groups of three (do they need to be comma delimited?
Nora
Dr N B Cronin X-Ray Laboratory Manager Tel. (+44) 020 7153 5445 Section of Structural Biology Fax. (+44) 020 7153 5456 Chester Beatty Laboratories mobile: (+44) 07787554059 The Institute of Cancer Research 237 Fulham Road London SW3 6JB
The Institute of Cancer Research: Royal Cancer Hospital, a charitable Company Limited by Guarantee, Registered in England under Company No. 534147 with its Registered Office at 123 Old Brompton Road, London SW7 3RP.
This e-mail message is confidential and for use by the addressee only. If the message is received by anyone other than the addressee, please return the message to the sender by replying to it and then delete the message from your computer and network. _______________________________________________ phenixbb mailing list [email protected] http://phenix-online.org/mailman/listinfo/phenixbb
Hi Nora, I'm sorry for the trouble! I tried your fixed ensemble command out with the current phenix and it ran fine for me. Could you possibly try downloading a very recent nightly build and see if that fixes the problem? If not, please let me know and we'll fix it. All the best, Tom T parameter file: ... fixed_ensembles { fixed_ensembleID_list = ensemble_1 fixed_euler_list = 87.09 64.28 257.24 fixed_frac_list = 0.54 0.079 0.069 fixed_frac_list_is_fractional = True } output: ... Adding Ensemble ensemble_1 as fixed solution with: Euler angles: [87.09, 64.28, 257.24] Coords (orthogonal A): [0.54, 0.079, 0.069] Keeping all solutions within 75.00 percent of the best solution Only searching in Space Group given in MTZ file plus opposite hand if enantiomorphic) Trying only input search order Disabling consistency check for all ensembles Starting PHASER ... Note: the "orthogonal A" is a typo I just noticed and I have now fixed that to say "fractional" in this case... ________________________________________ From: [email protected] [[email protected]] on behalf of Nora Cronin [[email protected]] Sent: Tuesday, May 01, 2012 7:32 AM To: PHENIX user mailing list Subject: Re: [phenixbb] Estimation of ligand binding affinity by occupancy refinement I'm having a small problem with format - entering fixed_ensembles in automr: my input: fixed_ensembles { fixed_ensembleID_list = "ensemble_1" fixed_euler_list = 87.09 64.28 257.24 fixed_frac_list = 0.540 0.079 0.069 fixed_frac_list_is_fractional = True } Phenix output: Adding Ensemble ensemble_1 as fixed solution with: Euler angles: [87.09, 64.28, 257.24] Coords (orthogonal A): [0.54, 0.079, 0.069] *************ERROR ENDING ******************* **************************************** AutoMR Input failed Python argument types in SOLU.addSOLU_6DIM_ENSE(InputMR_AUTO, str, list, bool, list, float, bool, bool, bool) did not match C++ signature: addSOLU_6DIM_ENSE(phaser::SOLU {lvalue}, std::string, scitbx::vec3<double>, bool, scitbx::vec3<double>, double, bool, bool, bool, bool, scitbx::vec3<double>, double) **************************************** *************ERROR ENDING ******************* [1 In addition to fixed two solutions is it necessary to repeat the key phrases or can one add to "fixed_euler_list" in groups of three (do they need to be comma delimited? Nora Dr N B Cronin X-Ray Laboratory Manager Tel. (+44) 020 7153 5445 Section of Structural Biology Fax. (+44) 020 7153 5456 Chester Beatty Laboratories mobile: (+44) 07787554059 The Institute of Cancer Research 237 Fulham Road London SW3 6JB The Institute of Cancer Research: Royal Cancer Hospital, a charitable Company Limited by Guarantee, Registered in England under Company No. 534147 with its Registered Office at 123 Old Brompton Road, London SW7 3RP. This e-mail message is confidential and for use by the addressee only. If the message is received by anyone other than the addressee, please return the message to the sender by replying to it and then delete the message from your computer and network. _______________________________________________ phenixbb mailing list [email protected] http://phenix-online.org/mailman/listinfo/phenixbb
participants (7)
-
Dale Tronrud -
Edward A. Berry -
Nora Cronin -
Pavel Afonine -
Terwilliger, Thomas C -
Timothy Springer -
Zoran Stefanic