BSTR521
Winter 2011
SOLVING THE PHASE
PROBLEM
2011 11 BSTR521 MIR-I V01
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Wim Hol
BSTR521
Winter 2011
BIOMACROMOLECULAR CRYSTALLOGRAPHY
NATURALLY OCCURING
SOURCES
GENE CLONING
& EXPRESSION
PURIFICATION
CRYSTALLIZATION
DATA COLLECTION
INITIAL PHASE DETERMINATION
MOLECULAR
REPLACEMENT
(MR)
MULTI-WAVELENGTH
ANOMALOUS DISPERSION
(MAD)
ISOMORPHOUS
REPLACEMENT
(MIR)
ELECTRON DENSITY IMPROVEMENT
MODEL BUILDING
STRUCTURE REFINEMENT
EVOLUTION
STRUCTURE ANALYSIS
VACCINE DESIGN
MECHANISMS
PROTEIN ENGINEERING
DRUG DESIGN
2011 11 BSTR521 MIR-I V01
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Winter 2011
Solving the phase problem in protein crystallography by de novo
methods
1A. The isomorphous replacement method
a) Multiple isomorphous replacement (MIR)
b) Single isomorphous replacement (SIR)
B. Isomorphous replacement enhanced by anomalous scattering
information
a) Multiple isomorphous replacement and anomalous scattering
(MIRAS)
b) Single isomorphous replacement and anomalous scattering (SIRAS)
2. Multi-wavelength anomalous dispersion (MAD) methods &
Single-wavelength anomalous dispersion (SAD) methods
a) Use of “intrinsic” anomalous scatterers such as occur in metallo
proteins and in SelenoMet proteins and even sulfurs!!
b) Use of “rational” “non-intrinsic” anomalous scatterers such as
brominated nucleotides
c) Use of heavy atom derivatives – but only one crystal needed!
3. Direct methods
Has so far been "only" successful in small proteins with resolution of data
beyond 1.2 Å.
4. “Umweg reflections” or “Renninger effect”
Keep one reflection permanently in reflection condition and rotate about
its reciprocal lattice vector S, then variations in its intensity can be
observed in favorable cases due to the fact that other reflections pass the
Ewald sphere. The variation in intensity provides information about the
phase difference between the two reflections which diffract
simultaneously.
(See Giacovazzo, “Fundamentals of Crystallography”, pp. 191-195 (1st Ed., 1991).)
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Multiple Isomorphous Replacement (MIR)
Basic Idea : Use a simpler problem (=finding the heavy atom sites) as a
stepping stone towards solving a very complicated one (=
finding all protein atoms)
Step 1. Prepare heavy atom (HA) derivatives
Step 2. Measure |FPH|
Step 3. Scale |FPH| vs. |FP| (assuming |FP| already measured )
Step 4. Find heavy atom positions by:
Difference Pattersons; Direct methods; Difference Fouriers
Step 5. Optional: refine HA-parameters without phase info
Step 6. Calculate phase probability
Step 7. Calculate best and figure of merit, m
Step 8. Optimize HA-parameters and back to 6 until convergence reached
Step 9. Calculate difference Fourier : m(FPH-FP)expibest
& residual Fourier:
m (FPHobs  FPHcalc ) exp i calc
PH
to complete HA-parameter set and optimize phase again
Step 10. Calculate ‘best’ Fourier : ( x )   m hkl | Fhklobs | exp i hkl
best
hkl
Note:
|FP| = the structure factor of the protein;
|FPH| = the structure factor of the HA derivative.
2011 11 BSTR521 MIR-I V01
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MIR: CAN A HEAVY ATOM COMPOUND GIVE A MEASURABLE
SIGNAL?
Crick & Magdoff derived in 1959:
I  2 N H 


I
 NP 
Where:
1
2
f 
 H 
 fP 
NH = number of heavy atoms
NP = number of protein atoms
fH = atomic scattering factor h. a.
fP = atomic scattering factor protein.
The effect of a single mercury is surprisingly large:
Mr of protein
14,000
28,000
56,000
112,000
224,000
448,000
896,000
1,792,000
I / I due to one Hg
I / I due to four Hg
0.51
0.36
0.25
0.18
0.13
0.09
0.06
0.045
1.02
0.72
0.50
0.36
0.26
0.18
0.13
0.09
So even multi-million Dalton proteins easily doable, in principle....
2011 11 BSTR521 MIR-I V01
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Intensity differences in diffraction patterns of native and derivative crystals of papain:
One half reflections from native papain crystal; one half from a papain crystal soaked
in mercury compound. Notice that the left-right mirror symmetry is broken but that the
upper-lower symmetry is maintained since the latter are crystallographically equivalent
and from the same crystal.
From:
http://www.esi.umontreal.ca/~syguschj/cours/BCM6200/BCM6200_Isomorphous%20Replacement.pdf
But: the original diffraction images combination from Jan Drenth, University of Groningen, The
Netherlands.
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MIR Step 1 : Preparation of Heavy Atom Derivatives
General comments:
- Classical “Medium Long Soaks”: see two pages below.
- Modern “Quick Soaks”: see two pages below.
(Even unfreezing a frozen crystal and soak in HA solution and
refreeze is a worthwhile idea – you might get annealing benefit
coupled with HA benefit (but in many cases the HA compound is
damaging your crystal)
- To backsoak or not to backsoak is a delicate question.
- Co-crystallization with heavy atom compounds is sometimes
spectacularly successful.
- K2PtCl4 single most successful HA compound?
- Change mother liquor, or pH, where needed or sensible.
- Beware of complexation of your beloved heavy atom compound by
your beloved additive, e. g. EDTA, azide, DTT, metal ions, phosphate
ions, etc.
- Know your protein perfectly. For instance, if it has a putative Ca-site
try lanthanides, or barium. If there are no or very few Cys then use sitedirected mutagenesis to introduce extra Cys to increase the probability
of binding a Hg, Au or other HA. If there are no His, introduce a few
His to increase probability of HA binding.
Basic texts:
- Blundell & Johnson - chpt. 8 - still full of insight.
- Bernard Rupp “Biomolecular Crystallography” (2010)
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MIR Step 1 : Preparation of heavy atom derivatives
(26)
465
SCREENING FOR HEAVY-ATOM DERIVATIVES
TABLE 1
MOST COMMONLY CITED HEAVY-ATOM DERIVATIZING REAGENTS AS COMPILED
FROM MACROMOLECULAR STRUCTURES FOR 1991-1994a
Reagent
K2PtCl4
KAu(CN)2
Hg(CH3COO)2
Pt(NH3)2Cl2b
UO2(CH3COO)2
HgCl2
K3UO2F5
Ethyl mercurithiosalicylatec
(K/NA)AuCl4
(Na/K)3IrCl6
CH3CH2HgPO4
K2PtCl6
UO2(NO3)2
K2Pt(NO2)4
(CH3)3Pb(CH3COO)
CH3HgCl
p-Chloromercuribenzene sulfonate
a
b
c
d
e
f
Citation
73
29
29
26
25
25
23
22
22
21
20
19
17
17
14
13
13
Reagent
K2Pt(CN)4
PIPd
Pb(CH3COO)2
K2HgI4
Mersalyt
p-Chloromercuribenzoate
CH3Hg(CH3COO)
TAMMe
SmCl3
K2OsO4
(K/Na)2OsCl6
UO2SO4
Baker's dimercurialf
2-Chloromercuri-4-nitrophenol
AgNO3
CH3CH2HgCl
p-Hydroxymercuribenzoate
Citation
12
12
12
12
12
11
11
10
8
8
7
6
6
6
5
5
5
The reagents are ranked by the number of times they were used in MIR or SIR
structure determinations, and do not necessarily reflect the quality of the derivatives.
From Ref. 10.
When specified, the cis isomer was used most often.
Thimerosal.
Di-m-iodobis(ethylenediamine)diplatinum.
Tetrakis(mercuriacetoxy)methane; C(HgOOCH3)4.
1,4-Diacetoxymercuri-2,3-dimethoxybutane.
Reagents are listed only with regard to their frequency of use, and not by any measure of their
usefulness in phasing. Some combinations of heavy atom reagents and stabilizing solution are not
recommended, because the heavy atom is bound by or reacts with the stabilizing solution; these
considerations are thoroughly discussed elsewhere.
From: Mark A. Roulp
"Screening for Heavy Atom Derivatives and obtaining Accurate Isomorphous Differences"
Methods in Enzymology, Vol. 276, p. 465 (1997) (Carter and Sweet, Eds)
2011 11 BSTR521 MIR-I V01
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Long, Medium and Quick Heavy Atom soaks.
In addition to the question which heavy-atom compounds (HACs) to
use, there is the question of which concentrations to use, and how long a soak
should last. The traditional procedures used to be 1 to 3 mM HAC
concentrations for 1-3 days at room temperature. This “medium” approach is
still a very useful initial guide. Some protein and nucleic acid crystals are
very sensitive to certain HACs, and then trying shorter times and lower
concentrations are worthwhile trying out. If no trace of a bound HAC is seen
in difference Pattersons, or in difference Fouriers, then higher concentrations
should be considered.
For certain Pb-containing HACs soaking times should be much longer,
in the order of a few weeks.
With the advent of flash-cooling of crystals in liquid nitrogen, a new
procedure is becoming popular: the “quick soak” method. Use high
concentrations of HACs but only for a minute or a few minutes, or in some
cases only a few seconds. There is ample evidence that small compounds can
lead to full occupancy in binding sites after soaking for only 10 seconds (E.g.
Bosch et al, J. Med. Chem. 49, 5939-5046 (2006)). Of course, if a slow
conformational change, or a slow chemical reaction, has to occur during
HAC binding then such short times might not work. The HAC
concentrations in the quick-soak method are usually quite high and would
destroy often the crystals when soaked for days as used in the traditional
medium procedure. But with flash freezing, crystals can often be rescued
before they are destroyed and give reasonable diffraction patterns and yield
good derivatives. Below are some papers which describe initial successes
with the quick-soak method, which was developed originally specifically
with anomalous diffraction difference-phasing (SAD and MAD) in mind.
Dauter, Z., Dauter, M. & Rajashankar, K. R. (2000). Novel approach to phasing proteins: derivatization by short
cryo-soaking with halides. Acta Crystallogr D Biol Crystallogr 56, 232-7.
Dauter, Z. & Dauter, M. (2001). Entering a new phase: using solvent halide ions in protein structure
determination. Structure 9, R21-6.
Nagem, R. A., Dauter, Z. & Polikarpov, I. (2001). Protein crystal structure solution by fast incorporation of
negatively and positively charged anomalous scatterers. Acta Crystallogr D Biol Crystallogr 57, 996-1002.
R. A., Polikarpov, I. & Dauter, Z. (2003). Phasing on rapidly soaked ions. Methods Enzymol 374, 120-37.
Dauter, M. & Dauter, Z. (2006). Phase determination using halide ions. Methods Mol Biol 364, 149-58.
2011 11 BSTR521 MIR-I V01
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Winter 2011
Noble Gases as Heavy Atom Derivatives
Although already tried out with crystals mounted at room temperature in
capillaries by Schoenborn, Watson & Kendrew, Nature 207, 28-30 (1965), in recent
years the use of xenon as heavy atom derivative has become quite popular even at
cryotemperatures. Xenon derivatives tend to be very isomorphous to the native crystals!
The success rate claimed is in the order of 50%! (Maybe better : was once in the order
of 50%...)
A nice example of Xenon SIRAS phasing is described by Machius et al., PNAS,
96, 11717-11722 (1999). In this particular case the protein crystal was prepared by
pressurizing the crystal with 500 psi of xenon gas for 15 minutes at room temperature.
The chamber was then decompressed within 15 seconds and the crystal flash-frozen in
liquid propane within another 5 seconds. The xenon-derivatized crystals diffracted to
1.9 Å.
Papers describing devices to prepare xenon-derivatized crystals are:
A simple device for studying macromolecular crystals under moderate gas pressures (0.1-10MPa).
Stowell, M. H. B., Soltis, S. M., Kisker, C., Peters, J. W., Schindelin, H., Rees, D. C., Cascio, D.,
Beamer, L., Hart, P. J., Wiener, M. C. & Whitby, F. G. J. Appl. Cryst. 29, 608-613 (1996).
Freeze-trapping isomorphous xenon derivatives of protein crystals. Sauer, O., Schmidt, A. & Kratky,
C. J. Appl. Cryst. 30, 476-486 (1997).
A cell for producing xenon-derivative crystals for cryocrystallographic analysis. Djinovic-Carugo, K.,
Everitt, P. & Tucker, P. A. J. Appl. Cryst. 31, 812-814 (1998).
Note: Xenon has an interesting but not large anomalous signal - yet, worth measuring.
However, krypton binds generally at the same sites as xenon, but has a significantly
larger anomalous signal at  = 0.87 Å and is therefore very interesting from a MADphasing perspective even though for krypton higher pressures seem to be required than
for xenon.
Relevant krypton papers are:
High-pressure krypton gas and statistical heavy-atom refinement: a successful combination of tools
for macromolecular structure determination. Schiltz, M., Shepard, W., Fourme, R., Prangé, T., De La
Fortelle, E. & Bricogne, G. Acta Cryst. D53, 78-92 (1997).
MAD phasing with krypton. Cohen, A., Ellis, P., Kresge, N. & Soltis, S. M. Acta Cryst. D57, 233-238
(2001).
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Winter 2011
MIR Step 2 : MEASURE DERIVATIVE DATA
MIR Step 3 : SCALING DERIVATIVE AND NATIVE DATA
* Must be done with very great care and with thorough analysis of results
since everything depends on small differences between FP and FPH.
* Analysis of fall-off of FP and FPH in 3 (almost) perpendicular directions
useful to detect suspicious differences in falloff. (Look e.g. at the
TRUNCATE output in the CCP4 suite of programs).
* Anisotropic scaling of FPH versus FP is the minimum one should do.
* Local scaling can sometimes do wonders.
* Scan for differences as function of FP : saturation effects might cause
problems.
* Be aware that one or two outrageous differences can make your difference
Patterson look like a checkerboard or a mountain ridge: always check for
outliers in the  FPH  FP  list.
2
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MIR Step 4 : LOCATING HEAVY ATOM POSITIONS
This is of course a crucial next step. If this fails everything later does not
apply. Be aware that in tough cases one needs to explore small differences
in intensities and hence great care in the measurement step is essential –
and the highest resolution might not be best sine then radiation damage
takes its toll. High resolution is not really required for this particular step
since in general the sites are far apart (of course not always!). For a 480K
Dalton case, 4.5 Å resolution was OK to find 30 and 70 sites in two
derivatives. Currently there are several powerful computational
procedures to find at least a subset of the HA sites, including:
- Direct Methods
Shake-and-Bake (or SNB) is among the most powerful among these. A
similar method is used by SHELXD with some Patterson information.
- Patterson Procedures
- By “hand” – sometimes works like a dream – in simple cases…
- Superposition methods
- Vector Search methods
The program SOLVE uses Patterson methods based on a previous
program HASPP.
Distinguish:
- No local symmetry present; e.g., only one subunit per asymmetric unit.
- Local (  non-crystallographic) symmetry present. Distinguish:
- polar local symmetry (e.g. “cyclic” such as 3, 5, 6, also called
C3, C5, C6, etc.)
- non-polar local symmetry (e.g. “dihedral” 222, 32, also called
D2, D3, etc.); or “cubic” (i.e. tetrahedral (T), octahedral (O), or
icosahedral (I))
- helical symmetry
- irregular (or indecent) symmetry where e.g. you have several
trimers but with non-intersecting axes… can be very tricky.
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MIR Step 4 : DIFFERENCE PATTERSON
The ideal Patterson to derive heavy atom positions from would have
2
coefficients FH .
However, the only measurements available are FP & FPH .
Therefore take
FPH  FP
as an estimate of FH .


In many cases this will be a poor estimate, i.e. in cases when FH  FP .


However, the estimate is excellent when FH // Fp , i.e. when  H   P
and also when  H   P   .

How well will FPH  FP
2011 11 BSTR521 MIR-I V01

2
2
approximate FH on average?
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Winter 2011
MIR Step 4 : DIFFERENCE PATTERSON

H





FPH  FP  CE  AC  AE  AD  DC  AE 
 Fp cos  P   PH   FH cos  PH   H   FP
 FH cos PH   H   FP 1  cos PH   P 
  P 
 FH cos  PH   H   2FP sin 2  PH

2


F
PH
(1)
(2)
(3)
(4)
2
   P 
2   PH   P 
 FP   FH2 cos2  PH  H   4FP2 sin 4  PH
  4FP FH sin 
 cos PH  H 
2
2




2
2
 FH cos   PH   H   noise
1
1
 FH2  FH2 cos 2  PH   H   noise
2
2
1
 FH2  theoretical noise
2


(5)
(6)
(7)
(8)
In practice, add measuring errors & non-isomorphism:
1
2
2
  FPH  FP   FH2 
Fiso
2
theoretical noise
+ measurement noise
+ non-isomorphous noise.
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MIR Step 4
Fig. 3. The Harker section at w=1/3 from the difference Patterson function for the
K2OsCl6 single-site derivative of porcine growth hormone (16). Peaks are contoured at
equal intervals with the first contour at one standard deviation of the entire map.
Number
1
2a
3
4
5
a
Table 2
Position of Interatomic Vectors
Representing Symmetry-Related Heavy Atoms
in a Unit Cell of Space Group P3221
Vector positions (u,v,w)
Symmetry operations used
 x, y, z    y, x  y, z  2 3
 x, y, z    x  y, x, z  1 3
 x, y, z   y, x, z
 x, y, z   x  y, y, z  1 3
 x, y, z    x, x  y, z  2 3
 x  y, x  2y,1 3
 2x  y, x  y, 2 3
 x  y, x  y,2z
 y,2 y,2z  2 3
 2x, x,2z  1 3
Vector position number 2 is related to that of number 1 by symmetry, thus it is not
unique.
Ref: Sherin S. Abdel-Meguid 1996 “Structure Determination Using Isomorphous Replacement” In: C.
Jones, B. Mulloy, and M.R. Sanderson (Eds.) Methods in Molecular Biology Volume 56:
Crystallographic Methods and Protocols, Humana Press, Totowa, New Jersey, pp153-171.
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MIR Step 4 :Solving a Patterson by “hand”
Space group P21.
1
1
I.e. In Harker section v  2 : u  2x  x  2 u
w  2z  z  1 w
2
But x & z with respect to which two-fold screw axis?
For first position: take your choice & thereby define origin not only in x & z
but also in y
For second position: use cross vectors (1-2) to obtain coordinates relative to
same origin as first position.
For each of the potential positions for site #2, the crossvector #1 to #2 is different.
Hence the crossvectors determine the position of site #2, once site #1 is placed.
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MIR Step 4 : Solving a Patterson by “hand”
Space group P21 21 21
Positions:
Vector:
Patterson symmetry.: Pmmm
1 :
x
2 :
1
2
3 :
4 :
2 - 1:
y
z
-y
z+ 12
-x
y+ 12
-z+ 12
x+ 12
-y+ 12
-z
1
2
-x
- 2x
3 - 1 : -2x
4 - 1:
1
2
-2y
1
2
-2y+ 12
Harker w =
1
2
-2z+ 12
Harker v =
1
2
-2z
Harker u =
1
2
1
2
Therefore, if Harker section w = 12 contains a peak at (u1, v1, 1 2 )
and Harker section v = 12 contains a peak at ( 12 -u1, 1 2 , w1)
and Harker section u = 12 contains a peak at ( 1 2 , 1 2 -v1, 1 2 -w1).
Then:
(u1, v1, w1)  (x1, y1, z1) of position 1, by using the 2-1, 3-1 and 4-1
equations for the vectors given above, but going from u,v,w to x,y,z..
Again: define origin with this first position & use cross-vectors to set other
position relative to the same origin.
The figure above shows the symmetry operations on the frequently occurring
space group P212121 (See the International Tables of Crystallography for full
explanation). This space group is surprisingly complex.
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MIR Step 5 :Refinement of Heavy Atom Parameters without phase information.
FPH



2
Q R   Whkl FP ,obs  FPH ,obs   FH ,calc
hkl

F
with: H ,calc 
and:
xj, yj, zj
Bj
Zj
Whkl

j


2
2

f j Z j exp  B j  sin   exp  2  i hx j  ky j  lz j 
2
= positional parameters position of atom j;
= isotropic temperature factor (sometimes aniso);
= occupancy (usually highly correlated with Bj);
2
=  FPH  FP  to give large differences most weight.
QR is quite weak in removing erroneous positions (the dreadful model-bias
problem). Hence Terwilliger & Eisenberg (1983) introduced the
origin-removed version of QR, called here QTE:




2
2
2
2
Q TE 
Whkl  FP,obs  FPH ,obs   FP,obs  FPH ,obs   k  FH ,calc  FH ,calc


hkl
k = 1 for centric, ½ for acentric reflections
w = weight factor - quite complex in QTE.


 
2
Note: QR can incorporate anomalous dispersion info, and is then called
“FHLE-refinement.”
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MIR I - APPENDIX
Solving a Patterson by “hand” in the presence of local symmetry.
Hemocyanin:
Space group P21
Particle point group 32, also called D3:
Rotation function showed that the local 3-fold runs approximately parallel to
the crystallographic 2-fold screw axis.
This was one of the derivatives in the structure determination of Panulirus
interruptus haemocyanin, which is a hexamer with 6 subunits of ~75kDa
each, about 450 kDa in total.
The K2PtCl4 difference Patterson yielded 4 sites found by hand. Total set
was 30 sites eventually. JMB 158, 457-483 (1982).
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MIR Step 4: Hemocyanin (ctd)
(Hexamer, with point group 32, in asymmetric unit of space group P21 with
local 3 fold parallel 21). In the top Fig. below left: A horizontal line means a
triangle of HA sites. Δ is the distance between two planes of triangles with
HA sites. On the right, a horizontal line means a plane with the endpoints of
vectors between two triangles with HA sites shown at the left.
3
Harker
3
3
Pseudo-Harker
Local Harker
3
Corresponding Patterson
Heavy atom arrangement
viewed
perpendicular to 21 = b-axis
0
0
0
0
0
0
Heavy atom sites viewed parallel to the 2-fold screw axis
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MIR Step 4 : Hemocyanin (ctd.)
* In the  F
K 2 PtCl 4
 Fnative
0.14, w  0)!

2
Patterson a major peak occurred at u  0, v =
* This suggested that two “heavy atom triangles” would be eclipsed!
* If this were the case then:
(1) the vector set of the “local Harker” v  0.14 should be similar to the
“local Harker” v  0;
(2) the “pseudo Harker” v  ½ -0.14  0.36 should share features with
the true Harker v = ½.
View of the arrangement of the major Pt-sites in P. interruptus heamocyanin down the
crystallographic two fold
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MIR Step 4 : How section v = 0.14 of the K2PtCl4 difference Patterson of
hemocyanin actually looked like:
(a)
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Winter 2011
MIR Step 4 : Hemocyanin - Section v = 0.00 of K2PtCl4 difference Patterson.
(b)
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Winter 2011
MIR Step 4 : Hemocyanin: K2PtCl4 difference Patterson.
Harker section v = ½.
(c)
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Winter 2011
MIR Step 4 : Hemocyanin: K2PtCl4 difference Patterson section v = 0.36.
This is in this special case a “pseudo Harker section”, since 0.36=0.50-014
(d)
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