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Overcoming Severe Diffraction Anisotropy . in Crystallographic Refinement. Michael Sawaya ACA Meeting Thursday, July 27, 2006, 4:35 PM Honolulu/Kahuku. c*. c*. mean |F| vs. resolution. a* b* c*. b*. a*. c*. c*. a* b* c*. a*. b*. Diffraction Anisotropy.

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## Michael Sawaya ACA Meeting Thursday, July 27, 2006, 4:35 PM Honolulu/Kahuku

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**Overcoming Severe Diffraction Anisotropy**in Crystallographic Refinement Michael Sawaya ACA Meeting Thursday, July 27, 2006, 4:35 PM Honolulu/Kahuku**c***c* mean |F| vs. resolution a* b* c* b* a* c* c* a* b* c* a* b* Diffraction Anisotropy diffraction strength differs with cell direction ANISOTROPIC ISOTROPIC**Diffraction anisotropy arises when then number of lattice**contacts is less in one cell direction than another Myohemerythrin (PDB ID 2MHR) crystal packing viewed from two orthogonal directions The crystal diffracts to 1.3 Å along b*, 1.7 Å along a* and c* Sheriff & Hendrickson, (1987) Description of overall Anisotropy in Diffraction from Macromolecular Crystals. Acta A43, 118-121. View perpendicular to b View parallel to b**Diffraction anisotropy presents two major problems to**crystallographers • Problem 1: choice of resolution boundaries of the data set • Clearly, one would like to chose an ellipsoidal boundary for anisotropic data. • a) Concentric ellipsoids more accurately describe the intensity contours of anisotropic data sets than do concentric spheres. • b) Reflection bounded by ellipsoidal shells will have the similar I/s and Rsym. • Currently available programs provide only spherical shells for selecting a resolution cutoff and reporting diffraction statistics. (An anisotropic B is allowed in Scala, but is not recommended because parameters for this option are likely to be poorly determined.) • Anisotropic data is best contoured using ellipsoidal shells**The inadequacy of spherical shells in reporting diffraction**statistics • Problem 1 (continued) • 1) Anisotropic data quality varies not only with resolution, but also with direction. • 2) Within a spherical shell, data quality (I/s,Rsym) will be highly varied depending on direction. For example… • 3) If one wishes to keep the strong data at high resolution, one is forced to accept the weak, poorly measured data bounded by the same spherical shell. • Accept bad I/s,Rsymin high shell • Must justify bad stats to peers • 4) If you discard the high resolution data, you discard the details of the electron density map. Which will it be? • Same data set as previous slide, but bordered by spherical shells**Problem 2: The need for an anisotropic scale factor for**comparing Fcalc & Fobs • Refinement of a structure against anisotropic data will stall at a high R-factor • the agreement between Fobs and Fcalc will be very poor • |Fobs| has a directional dependence and |Fcalc| does not; • An anisotropic scale factor must be applied to either |Fobs| or |Fcalc| to make them comparable. • Anisotropic diffraction is not modeled by TLS disorder parameters nor individual isotropic B-factors. c* c* Areas of poor agree-ment b* b* | Fcalc | |Fobs | plane h=0 plane h=0**anisotropic B factor**Scale factor Scale factor Scale factor resolution resolution resolution b22= -5 Å2 b33= +12 Å2 b11= +2 Å2 along a*along b*along c* How the anisotropic scale factor works. B=12 Å2 • An anisotropic scale factor is a multiplicative factor like the overall B-factor. • Like the overall B-factor, its value varies with resolution. • But, unlike the overall B-factor, its value also varies with direction. • It has three principle components, b11, b22, and b33 acting as B-factors along a*,b*,c* directions, respectively. • An anisotropic data set can be made isotropic by applying the appropriate scale factor that increases |F| in weak diffracting direction or decrease |F| in the strong diffracting direction or a combination of both. • “B”s can be positive or negative. Same for all lattice directions (a*,b*,c*) Scale factor resolution isotropic B factor**[**] b11b12b13 b12b22b23 b13b23b33 c* a* b* Anisotropic Scale Factor Anisotropic tensor The anisotropic scale factor components are obtained from a least-squares fit of the elements of an anisotropic tensor to Fobs. S(|Fobs|-k|Fcalc|)2→ min k=e-(b11a*2h2+2b12a*b*hk+2b12a*c*hl+b22b*2k2+2b23b*c*kl+b33c*2l2) The value of k changes in the form of concentric elliptical shells from the center of the reciprocal lattice.The parametersb11b22andb33correspond to the principal axes of the ellipse. Anisotropic scaling is increasingly employed in crystallography. • Molecular replacement • Phaser (MR_ANISO keyword) • Refinement • Refmac • CNS • Anisotropic scaling dramatically improves R-factors (see The Effect of Overall Anisotropic Scaling in Macromolecular Refinement. Murshudov, Davies, Isupov, Krzywda and DodsonCCP4 Newsletter on Protein Crystallography Number 35. July 1998) , • But, a shortcoming in its formulation was newly revealed by the severe degree of anisotropy in our data set… and refinement was stalled.**Crystal structure of a PE-PPE protein complex from M.**tuberculosis. • PE and PPE are 2 families named for the conserved proline (P) and glutamate residues (E) near the N-termini. • Large families • 100 PE members • 60 PPE members • Precise function not known • Associated with cell wall • Linked to virulence • Immune evasion by antigenic variation? • Prevalent in M.tb. and absent in humans • Drug target Domain organization of the PE and PPE proteins as reported in Nature 393:537-44. (1998)**PE-PPE project**• Michael Strong • Characterization of the complex • 28 different individual proteins tested –insoluble. • A complex of Rv2430c and Rv2431c guided by bioinformatics • Purification • Crystallization and Structure Solution**Rebecca Page Screen**14% iso-Propanol 0.07M Sodium Acetate trihydrate pH 4.6 0.14M Calcium Chloride dehydrate 30% Glycerol anhydrous PE-PPE Crystal parameters • Crystals are plates • Selenomethionine derivative for MAD • Long, rod shaped unit cell a=40.8 b=46.7 c=283.1 Two complexes/asu • Space group P2221 • Fairly rare in PDB (0.03%) • Solvent content 42%**mean |F| vs.**resolution a* b* c* PE-PPE crystals diffract anisotropically c -strong a- medium b-weakest ALS beamline 8.2.2**Data used for phasing and refinement**• Using standard spherical bins of resolution**Data statistics for best data set**R-sym In highest resolution shell I/s Resolution (Å)**Phasing Statistics**• Just adequate**2.4 Å experimental electron density map**• Connectivity good enough to see the helical fold. • Side chain density is weak or non existent. • Use Se sites as reliable markers for sequence registration • Go forward with refinement…maps should improve. PE protein PPE protein PPE motif**Refinement yields only marginal improvement in electron**density map • Side chain density is still missing • Refinement stuck • Rwork=38.5% • Rfree=43.4% • No apparent way to improve the coordinates/R-factors. • No new features apparent in electron density map. • Check for twinning • Twinning not indicated • Check for pseudosymmetry • Refinement in P21 or P1 yielded no improvement in R factors • Use TLS • Unstable, R-factor shot up. • Use 3.0 Å cutoff • R-factors improved, but map does not improve. 2Fo-Fc Experimental 2.2 Å 2.4 Å**Looking to the literature for help**Science, vol 300, pp. 1256-1262 • Lodowski et al. Supplemental methods, • “Because the diffraction pattern exhibited severe anisotropy, a 3-D ellipsoid was defined and merging R-factors and I/s were calculated in ellipsoidal shells. Diffraction data were then limited to the outermost shell that still contained significant data…” • Zhang et al. • “Data observed to 2.5A resolution in the c* direction, but to only 3.3 A in the plane perpendicular to c*.” • An ellipsoid of diffraction data, rather than the usual sphere, was used for scaling and refinement. • Refers to Lodowski et al. for method. • Let’s do the same Acta D, vol 60, pp. 1512-1518**Solution proposed by literature**Equation of an ellipsoid 1=x2/a2 + y2/b2 + z2/c2 Where a, b, and c are the vertices of the ellipse. Set the following: a= 1/resolution limit along a*=1/2.2Å b=1/resolution limit along b*=1/3.2Å c=1/resolution limit along c*=1/2.2Å Resolution limits determined by the point were mean |F|/s drops below 2 for the given axis. See truncate output. To test whether a given reflection falls within the ellipsoid, calculate: x=component of d* along a* y=component of d* along b* z=component of d* along c* Plug a,b,c,x,y,z into equation above. Where the sum>1, discard reflection. Reflections before truncation 27,293 Reflections after truncation 20,053 discard discard**Big drop**R-work Before truncation After truncation Elliptical truncation produced a sharp drop in R-factors but no improvement in map. • Elliptical truncation yielded a • 6.0% drop in Rwork • 7.2% drop in free Rfree • Details: • Rwork= 38.5%→32.5% • Rfree = 43.4%→36.2% • TLS refinement is now stable, so it also contributes to improvement in R-factors. • Most of the drop is in the high resolution shells 3.0-2.2Å, where much of the poorly measured data was discarded. • 2Fo-Fc maps are still not improved. • Side chain density is still blobby as if only 3.5A resolution. • No new features. Can’t improve model! Panic!! • Clue: Average B of model coordinates =75 Å2. An effect artificially produced by the anisotropic scale factor.**Adverse Side Effect of Anisotropic Scaling**Fobs after scaling Fobs • The effect of anisotropic scaling was observed by plotting the scaled |Fobs|as a pseudo precession photograph; appearance was compared before and after scaling. • The adverse side effect of anisotropic scaling is to diminish the amplitude of well measured, high resolution reflections in the a*c* plane. • These reflections contribute almost nothing to the electron density because anisotropic scaling diminished their amplitudes. • The diminished contribution of these high resolution |Fobs| to the Fourier synthesis results in a map that appears to be low resolution. b* b* c* c* Isotropic, but high resolution |F|obs near c* are diminished**Why anisotropic scaling might diminish high resolution**|Fobs| • Imagine an ellipsoidal shell (Red ellipsoid) encapsulating all reflections in the data set were |Fobs|>2. • The goal of anisotropic scaling is to transform the ellipsoid into a sphere (Blue sphere) by scaling |Fobs| by the “appropriate amounts” in the three principal directions. • The “appropriate amounts” may be derived from 3 different approaches: • decrease |Fobs| in the strong diffracting directions (SBij≥0) • Increase |Fobs| in the weak diffracting directions (SBij≤0) • A combination of both of the above (SBij=0). • The choice of approach appears arbitrary; the results differ only by an isotropic B-factor (i.e. the radii of the blue spheres). • REFMAC encodes the last option, constraining the amplitude gains in the weak diffracting direction to be equal to the amplitude decreased in the strong diffracting direction. • Mathematically, this is equivalent to constraining the sum of the principle components of the anisotropic scale factor to be zero. • i.e. B11+B22+B33=0.0 SBij≥0 SBij≤0 SBij=0 B11 (Å2): + - -- B22 (Å2): 0 - -- B33 (Å2): +++++0 REFMAC**x**x Constraining SBij≤0 improved map, model building resumed. • It seemed important to maintain the contribution of the well measured, high resolution reflections in the a*c* plane so that they may contribute to the electron density map and reveal new details. • Of the three approaches, this effect can be best achieved by the constraint SBij≤0. • In practice, the SBij≤0 constraint was achieved by first applying the REFMAC derived anisotropic scale factor to |Fobs|, followed by a negative isotropic B-factor (-10Å2). • The anisotropically scaled |Fobs| was used as input for REFMAC refinement. SBij≤0 SBij≥0 SBij=0 B11 (Å2): + - -- B22 (Å2): 0 - -- B33 (Å2): +++++0 REFMAC**2Fo-Fc maps showed a marked improvement.**• 2Fo-Fc maps began to reveal carbonyl bumps, side chain density, and the presence of 72 waters, where previously we could see none. 2Fo-Fc using Automatic Anisotropic Scaling 2Fo-Fc using Improved Anisotropic Scaling**Elliptical truncation produced a sharp drop in R-factors but**no improvement in map. • Further model building yielded a • 7.7% drop in Rwork • 4.9% drop in free Rfree • Details: • Rwork= 38.5%→32.5% →24.8% • Rfree = 43.4%→36.2% →31.3% • R-factor dropped in both high and low resolution shells Before truncation After truncation R-work After negative B-factor correction and additional refinement R-factor improved throughout resolution range**Refinement statistics**• final**Origins of diffraction anisotropy resemble those in**myohemorythrin Strong diffraction Poor diffraction**Anisotropic scaling of other proteins**• The technique of applying anisotropic scaling with SBij≤0 has helped in the refinement of structures of Actin dimer, and Tim8/13 complex. • The improvement in R-factors and electron density maps have been more modest in these cases, as the anisotropy is less severe. • The technique appears to be most helpful when the best and worst diffracting directions extend between 2.5 to 3.0, where water molecules are discernable.**Procedures**• Judge whether anisotropy is a problem. • Look at the anisotropy graph from truncate (loggraph truncate.log) • Does mean F/s drop with different slopes along the 3 principle directions? • If anisotropy is significant, determine the resolution limits along the three principle cell directions. • Note where mean F/s drops below 2 along the three principle directions. • Truncate data using ellipsoidal limits. • I’ll make my truncation program available from http:www.doe-mbi.ucla.edu/~sawaya. • Calculate the anisotropic scale parameters (for Fcalc). • Perform a cycle of refinement with Refmac or CNS. • Note the anisotropic scale parameters (B11,B22,B33,etc.) listed in the PDB header • For example B11= -6, B22= +14, B33= -9 • Apply the negated scale factors to Fobs to create an isotropic data set. • For example B11= +6, B22= -14, B33= +9 • use cad from CCP4 • Apply a negative isotropic scale factor to the newly isotropic Fobs to restore the magnitude of those reflections weakened by the previous step. • Negate the most positive component from the previous step (e.g. +9 → -9). • Use cad again. • Use this scaled Fobs for refinement. • -all these steps are performed by the diffraction anisotropy server • http://www.doe-mbi.ucla.edu/~sawaya/anisoscale/**Acknowledgements**• Michael Strong • Shuishu Wang • Duilio Cascio • Alex Lisker • David Eisenberg

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