Phasing

1
Phasing

• Goal is to calculate phases using isomorphous and
  anomalous differences from PCMBS and GdCl3
  derivatives --MIRAS.
• How many phasing triangles will we have for each
  structure factor?
• For example. FPH FPFH for isomorphous
  differences
• For example. FPH FP FH for anomalous
  differences
• -h-k-l hkl
  -h-k-l

2
4 Phase relationships

• PCMBS FPH FPFH for isomorphous differences
• PCMBS FPH FP FH for anomalous differences
• -h-k-l hkl
  -h-k-l
• GdCl3 FPH FPFH for isomorphous
  differences
• GdCl3 FPH FP FH for anomalous
  differences
• -h-k-l hkl
  -h-k-l

3
SIR Phasing Ambiguity
PCMBS FPH FPFH for isomorphous differences
Imaginary axis
Fp
FPH
Real axis
FH
Harker construction for SIR phases. FP native
measurement FH (hkl) calculated from heavy atom
position. FPH(hkl)measured from derivative.
Point to these on graph.
4
Harker Construction for SIRAS phasing (Single
Isomorphous Replacement with Anomalous Scattering)
PCMBS FPH FP FH for anomalous differences
-h-k-l hkl -h-k-l
Imaginary axis
Isomorphous differences Anomalous differences
Fp (hkl)
FH(-h-k-l)
Real axis
We will calculate SIRAS phases using the PCMBS Hg
site. FP native measurement FH (hkl) and
FH(-h-k-l) calculated from heavy atom
position. FPH(hkl) and FPH(-h-k-l) measured from
derivative. Point to these on graph.
FH(hkl)
5
Harker Construction for MIRAS phasing (Multiple
Isomorphous Replacement with Anomalous Scattering)
GdCl3 FPH FPFH for isomorphous
differences
Imaginary axis
Isomorphous Deriv 2
Fp (hkl)
Anomalous Deriv 1
Real axis
Isomorphous Deriv 1
6
Harker Construction for MIRAS phasing (Multiple
Isomorphous Replacement with Anomalous Scattering)
GdCl3 FPH FP FH for anomalous
differences -h-k-l
hkl -h-k-l
Imaginary axis
Isomorphous Deriv 2
Fp (hkl)
Anomalous Deriv 1
Real axis
Isomorphous Deriv 1
Anomalous Deriv 2
7
Barriers to combining phase information from 2
derivatives

1. Initial Phasing with PCMBS
2. Calculate phases using coordinates you
   determined.
3. Refine heavy atom coordinates
4. Find Gd site using Cross Difference Fourier map.
5. Easier than Patterson methods.
6. Want to combine PCMBS and Gd to make MIRAS
   phases.
7. Determine handedness (P43212 or P41212 ?)
8. Repeat calculation above, but in P41212.
9. Compare map features with P43212 map to determine
   handedness.
10. Combine PCMBS and Gd sites (use correct hand of
    space group) for improved phases.
11. Density modification (solvent flattening
    histogram matching)
12. Improves Phases
13. View electron density map

8
Center of inversion ambiguity

• Remember, because the position of Hg was
  determined using a Patterson map there is an
  ambiguity in handedness.
• The Patterson map has an additional center of
  symmetry not present in the real crystal.
  Therefore, both the site x,y,z and -x,-y,-z are
  equally consistent with Patterson peaks.
• Handedness can be resolved by calculating both
  electron density maps and choosing the map which
  contains structural features of real proteins
  (L-amino acids, right handed a-helices).
• If anomalous data is included, then one map will
  appear significantly better than the other.

Patterson map
9
Use a Cross difference Fourier to resolve the
handedness ambiguity
With newly calculated protein phases, fP, a
protein electron density map could be calculated.
The amplitudes would be FP, the phases would
be fP. r(x)1/VSFPe-2pi(hxkylz-fP) Answe
r If we replace the coefficients with FPH2-FP,
the result is an electron density map
corresponding to this structural feature.
10
r(x)1/VSFPH2-FPe-2pi(hx-fP)

• What is the second heavy atom, Alex.
• When the difference FPH2-FP is taken, the protein
  component is removed and we are left with only
  the contribution from the second heavy atom.
• This cross difference Fourier will help us in two
  ways
• It will resolve the handedness ambiguity by
  producing a very high peak when phases are
  calculated in the correct hand, but only noise
  when phases are calculated in the incorrect hand.
• It will allow us to find the position of the
  second heavy atom and combine this data set into
  our phasing. Thus improving our phases.

11
Phasing Procedures

1. Calculate phases for site x,y,z of PCMBS and run
   cross difference Fourier to find the Gd site.
   Note the height of the peak and Gd coordinates.
2. Negate x,y,z of PCMBS and invert the space group
   from P43212 to P41212. Calculate a second set of
   phases and run a second cross difference Fourier
   to find the Gd site. Compare the height of the
   peak with step 1.
3. Chose the handedness which produces the highest
   peak for Gd. Use the corresponding hand of space
   group and PCMBS, and Gd coordinates to make a
   combined set of phases.

12
Lack of closure
e(FHFP)-(FPH)
FH-calculated from atom position
FP-observed
FPH-observed
e is the discrepancy between the heavy atom model
and the actual data.
Why is it not zero?
13
Phasing power
FH/ e phasing power. The bigger the
better. Phasing power gt1.5 excellent Phasing
power 1.0 good Phasing power 0.5 unusable
e(FHFP)-(FPH)
14
Rcullis

• /FPH-FP Rcullis.
• Kind of like an Rfactor for your heavy atom
  model. FPH-FP is like an observed FH, and e
  is the discrepancy between the heavy atom model
  and the actual data.
• Rcullis lt1 is useful. lt0.6 great!

e(FHFP)-(FPH)
15
Figure of Merit
0


270
90
180
0

270
90

180
Phase probability distribution
How far away is the center of mass from the
center of the circle?
16
Density modification

• A) Solvent flattening.
• Calculate an electron density map.
• If rltthreshold, -gt solvent
• If rgtthreshold -gt protein
• Build a mask
• Set density value in solvent region to a constant
  (low).
• Transform flattened map to structure factors
• Combine modified phases with original phases.
• Iterate
• Histogram matching

17
Density modification

• B) Histogram matching.
• Calculate an electron density map.
• Calculate the electron density distribution.
  Its a histogram. How many grid points on map
  have an electron density falling between 0.2 and
  0.3 etc?
• Compare this histogram with ideal protein
  electron density map.
• Modify electron density to resemble an ideal
  distribution.

Number of times a particular electron density
value is observed.
Electron density value
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HOMEWORK