Michael Sawaya

1
Overcoming Severe Diffraction Anisotropy
in Crystallographic Refinement
Michael Sawaya ACA Meeting Thursday, July 27,
2006, 435 PM Honolulu/Kahuku
2
Diffraction Anisotropy
diffraction strength differs with cell direction
ANISOTROPIC
ISOTROPIC
3
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
4
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

5
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, Rsym in 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

6
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 h0
plane h0
7
How the anisotropic scale factor works.
B12 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.
• Bs can be positive or negative.

Same for all lattice directions (a,b,c)
Scale factor
resolution
isotropic B factor
8
Anisotropic Scale Factor

• The anisotropic scale factor components are
  obtained from a least-squares fit of the elements
  of an anisotropic tensor to Fobs.
• S(Fobs-kFcalc)2 ? min
• ke-(b11a2h22b12abhk2b12achlb22b2k22b23b
  cklb33c2l2)
• The value of k changes in the form of concentric
  elliptical shells from the center of the
  reciprocal lattice. The parameters b11 b22 and
  b33 correspond 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 Dodson CCP4
  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.

Anisotropic tensor
9
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 393537-44. (1998)
10
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

11
PE-PPE Crystal parameters

• Crystals are plates
• Selenomethionine derivative for MAD
• Long, rod shaped unit cell
• a40.8
• b46.7
• c283.1
• Two complexes/asu

• Space group P2221
• Fairly rare in PDB (0.03)
• Solvent content 42

12
PE-PPE crystals diffract anisotropically
?
?
c -strong a- medium b-weakest
ALS beamline 8.2.2
13
Data used for phasing and refinement

• Using standard spherical bins of resolution

14
Data statistics for best data set
R-sym
In highest resolution shell
I/s
Resolution (Å)
15
Phasing Statistics

• Just adequate

16
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 refinementmaps should improve.

PE protein PPE protein PPE motif
17
Refinement yields only marginal improvement in
electron density map

• Side chain density is still missing
• Refinement stuck
• Rwork38.5
• Rfree43.4
• No apparent way to improve the coordinates/R-facto
  rs.
• 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
18
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.
• Lets do the same

Acta D, vol 60, pp. 1512-1518
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Solution proposed by literature
Equation of an ellipsoid 1x2/a2 y2/b2
z2/c2 Where a, b, and c are the vertices of the
ellipse. Set the following a 1/resolution
limit along a1/2.2Å b1/resolution limit along
b1/3.2Å c1/resolution limit along
c1/2.2Å 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 xcomponent of d along a ycomponent
of d along b zcomponent of d along c Plug
a,b,c,x,y,z into equation above. Where the sumgt1,
discard reflection. Reflections before
truncation 27,293 Reflections after truncation
20,053
discard
discard
20
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. Cant improve model! Panic!!
• Clue Average B of model coordinates 75 Å2. An
  effect artificially produced by the anisotropic
  scale factor.

21
Adverse Side Effect of Anisotropic Scaling
Fobs after scaling

• 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 ac 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.

Fobs
?
?
b
b
c
c
Isotropic, but high resolution Fobs near c are
diminished
22
Why anisotropic scaling might diminish high
resolution Fobs

• Imagine an ellipsoidal shell (Red ellipsoid)
  encapsulating all reflections in the data set
  were Fobsgt2.
• 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. B11B22B330.0

SBij 0
SBij 0
SBij 0
B11 (Å2) - -- B22 (Å2)
0 - -- B33 (Å2)
0
REFMAC
23
Constraining SBij0 improved map, model building
resumed.

• It seemed important to maintain the contribution
  of the well measured, high resolution reflections
  in the ac 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 SBij0.
• In practice, the SBij0 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
24
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
25
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
26
Refinement statistics

• final

27
Origins of diffraction anisotropy resemble those
in myohemorythrin
Strong diffraction
Poor diffraction
28
Anisotropic scaling of other proteins

• The technique of applying anisotropic scaling
  with SBij0 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.

29
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.
• Ill make my truncation program available from
  httpwww.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

30
Acknowledgements

• Michael Strong
• Shuishu Wang
• Duilio Cascio
• Alex Lisker
• David Eisenberg