Fitting atomic models into EM map Alexei Vagin Alexei Vaguine alternative spelling York Structural B

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Fitting atomic models into EM map Alexei
Vagin( Alexei Vaguine alternative spelling
)York Structural Biology LaboratoryUniversity
of York
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lt-- models
result
EM
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Molecular replacement
put homologous model into crystal with unknown
structure or Atomic Model --gt EM map
1) 6 - dimensional search check all
orientations and positions

• 3-d 3-d search
• orientations positions
• Conventional Molecular Replacement

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Molecular replacement programs and systems

• Programs Systems
• Amore MrBump
• MOLREP Phenix
• QS BALBES
• PHASER
  Many others
• EPMR
• CNS
• URO

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Functions of molecular replacement

• Cross Rotation function
• Self Rotation function
• Translation function
• Phased Translation function
• Fast Packing function

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Cross Rotation Function
map
model
Patterson
Pmod
Pobs
RF
RF(?) ? Pobs(r) R? Pmod(r) dr
R? - rotation operator
?
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Optimal radius of integration
map
model
B
A
Vinter
AB
BA
Diametre of model
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Self Rotation Function
map
RF(?) ? Pobs(r) R? Pobs(r) dr
a
RF
a
?
0
90
a
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Self Rotation Function
Space group P21 one tetramer
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Translation Function

• TF(s) ? Pobs(r) Pcalc(s,r) dr

s - vector of translation
Phased Translation Function
PTF(s) ? ?obs(r) ?calc(s,r) dr
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Fast Packing Function
Estimation of overlap

Packing function
K j
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Questions
How to use X-ray data

• Maximum resolution limit ?
• Minimal resolution limit ?
• Weighting scheme ?

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Short introduction toFourier Transformation
Operators
addition
? F ?
addition
product
convolution
? F ?
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Functions
Real function
Complex function
? F ?
? F ?
Gaussian
Gaussian
A
1/A
? F ?
Grid
Grid
1/A
A
? F ?
Step function
Interference function
A
1/A
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Crystal and Structure Factors
Reciprocal space
? F ?
Real space
Fobs(s)
s
1/A
A
Product
? F ?
Convolution
Fh
h
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Real space
? F ?
Reciprocal space
Map ?(r)
F(s) structure factors
? F ?
? F ?
product
convolution
F(s) F(s) I(s)
inensities
? F ?
Patterson P(r)
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High resolution data

• High resolution limit from Optical resolution
• Weights for high resolution data

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Optical resolution
Reciprocal space
Real space
? F ?
Fobs(s)
?
atm
?
res
resmax
?
?
res 0.356 resmax
Single peak
2 atm2 res2
?
?
?
?
Optres 2
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Optical resolution from origin peak of Patterson
Patterson
Real space
?
patt
atm
?
?
Optres 2 atm
?
?
?
atm2 ( patt2 res2 )/2
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Optical Resolution Å
?
Optres 2
2 ( atm2 res2 ) )/2
?
?
?
Å
5
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Resolution
Optimal high resolution limit
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Optical Resolution ( by sfcheck )
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Weights for high resolution data and similarity
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1
2
Fobs(s)
Map
2?
Model
1
2
1-2
2-1
2-2
1-1
PTF
1
2
Map (blurred)
Fobs(s)
Exp(-Bs2)
?
B1/4 2 2
?
1-2
2-1
1-1 2-2
PTF
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Low resolution data

• Weights for low resolution data and
• size of model

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Soft minimal resolution cut-off
Real space
Reciprocal space
? F ?
Fobs(s)
s
Radmodel
Exp(-Bs2)
Exp(-r2/2 2)
?
B1/4 2 2
?
?
?
Radmodel / 6
product Exp(-Bs2) Fobs
convolution
subtraction
(1-exp(-Bs2) )Fobs
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Weighting scheme
Fused (1 - exp(-Boffs2) ) Fobs
exp(-Bs2)
1 - exp(-Boffs2)
1
exp(-Bs2)
s
1/Rmin
1/Rmax
Rmin v2Boff 2 model model
Radmodel / 6
?
?
B1/4 2 2
?
?
?
Model similarity
Rmax v2B
Rmin Radmodel
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Weighting scheme
Two filters in Image
processing Gaussian highpass filter
Gaussian lowpass filter
exp(-Bs2)
Fused (1 - exp(-Boffs2) ) Fobs
We can consider this weighting scheme as an
approximation to the likelihood approach
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Information in X-ray and Model must overlap
1
s
1/Rmin 1/Rmax
(fom model similarity)
(fom model size)
1/Resmax_used (fom opt. resolution)
1/Resmin_X-ray
1/Resmax_X-ray
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Can we find solution?
Weight of low resolution grows Low
high Model
Similarity 0 .1 0.2 0.3 0.4
0.5
Very likely
Weight of high resolution grows Low
high Model size 0.5
0.4 0.3 0.2 0.1
Very unlikely
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What do you need to do before MR

• 1) Examine the data
• 2) Examine the model

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Examine the data (e.g by sfcheck)

• Completeness of data
• signal-to-noise
• Anisotropy (make correction?)
• Pseudo-translation
• Twinning
• Resolution

• Keep in mind for EM map
• Map scale factor
• Handedness of map

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Examine the model

• Look at the molecular shape and flexibility
• Check the sequence similarity
• Estimate the model size
• Choose the method of the model correction
• Estimate number of copies

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Example model ? EM
6-mer hemocyanin
Ulrich Meissner et al. J.Mol.Biol. (2003) 325,
99-109
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EM map
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EM map (sfcheck 1)
From grid
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EM map (sfcheck 2)
9A
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Model
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Rotation Function
Radius of int 50.72 Resmin,Resmax 212.00
8.96 theta phi chi Rf/sigma
Sol_ 1 52.25 -110.27 166.40 3.98 Sol_
2 75.76 -170.07 108.38 3.98 Sol_ 3
117.46 129.68 124.90 3.97 Sol_ 4 66.32
11.00 85.03 3.97 Sol_ 5 38.59
71.16 164.30 3.97 Sol_ 6 129.34 -48.80
105.84 3.97 Sol_ 7 123.98 -46.97
121.08 3.37 Sol_ 8 75.79 13.02 96.32
3.37 Sol_ 9 125.43 134.59 116.16 3.37
Sol_ 10 51.15 47.70 155.97 3.37 Sol_ 11
44.47 -105.43 161.40 3.37 Sol_ 12
47.16 73.03 159.71 3.35 Sol_ 13 122.50
-72.37 129.46 3.35
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Translation Function 1
Sol_--- phased translation function ---Sol_
Resmin,Resmax 212.00 8.96S_ RF TF
tx ty tz ScoreS___2__1 1
0.405 0.362 0.600 0.189 S___4__1 2
0.435 0.636 0.601 0.179 S___1__1 3
0.659 0.473 0.600 0.179 S___5__1 4
0.595 0.361 0.381 0.177 S___3__1 5
0.565 0.636 0.380 0.174 S___6__1 6
0.341 0.472 0.381 0.169 S___7__1 7
0.569 0.630 0.359 0.081S___9__1 8 0.432
0.630 0.617 0.077. . . . . . . . . .
Number of monomers in fixed model 1
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Translation Function 2
S_ RF TF tx ty tz
Score S___1__1 1 0.341 0.473 0.381
0.260 S___4__1 2 0.435 0.636 0.601
0.260 S___3__1 3 0.659 0.473 0.600
0.257 S___5__1 4 0.565 0.636 0.380
0.255 S___6__1 5 0.594 0.361 0.381
0.249 S___7__1 6 0.569 0.630 0.359
0.186S___9__1 7 0.655 0.478 0.621
0.185S___8__1 8 0.434 0.631 0.616
0.184 . . . . . . . Number of monomers in
fixed model 2
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Translation Function (final)
S_ RF TF tx ty tz
Score S___6__1 1 0.594 0.361 0.380
0.441 S___8__1 2 0.588 0.362 0.362
0.421S___9__1 3 0.629 0.281 0.328
0.421 . . . . . . . . Number of monomers in
the model 6
For mirror map
Rotation function the same
Translation function (1 step)
correct peaks
incorrect Score 0.060 - 0.057
0.068
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Result
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We can have a problem with RF if completeness of
model is low
Alternative approach
1. To find the position 2. To find the
orientation
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Spherically Averaged Phased Translation Function
(SAPTF)
radial distribution
Map
? (r)
? m(r)
? s(r)
? m(r)
s
Model
SAPTF(s) ? ?s(r) ?m(r) r2 dr
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SAPTF as Fourier series
By expanding SAPTF into spherical harmonics it is
possible to represent it as a Fourier series
SAPTF(s) ? ?s(r) ?m(r) r2 dr
?h Ah exp(2 i hs)
?
Ah ?n Fhc00n(R) j0(2 Ra) b00n
?
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Algorithm
1. Find position Spherically averaged
phased translation function 2. Find
orientation Local phased rotation
function 3. Check and refine position
Phased translation function
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Example 2
13 subunits of Portal protein of
bacteriophage SPP1
Fred Antson at al. University of York
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EM map
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EM map (sfcheck 1)
from grid
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EM map (sfcheck 2)
8A
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model
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(No Transcript)
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SAPTF
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Spherically Average Phased Translation
Function
Correct peak numbers 496, 511, 515, . . .
Phased Rotation Function
Correct peak numbers 40, 59, 68, 85, 86, 90,
107, 111, 112
Phased Translation Function
correct peaks
incorrect Score 0.092 - 0.083
0.038
Final number of monomers 9
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Result with 9 monomers
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Spherically Average Phased Translation
Function with 13-fold symmetry
Correct peak number 36
(peaks were selected according 13-fold NCS)
Phased Rotation Function
Correct peak number 8
Phased Translation Function
correct peak
incorrect Score 0.083
0.042
Final number of monomers 13
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Result 1
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Result 2
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Result 3
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Rigid Body Refinement
Additional possibilities
1 In reciprocal space with phases
2 multi-domain refinement
3 use NC Symmetry as constraint
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Acknowledgments

• Gleb Bourenkov MPG-DESY, Hamburg . . . . . . .
  .1st friend
• Sasha Popov EMBL, Hamburg . . . . . . . . . . .
  . . . .2nd friend
• Misha Isupov University of Exeter . . . . . . .
  . . . . .3rd friend
• Andrey Lebedev YSBL, York . . . . . . . . . . .
  . . . .consultant
• Garib Murshudov YSBL, York. . . . . . . . . . .
  . . . . . .director
• BBSRC, CCP4 . . . . . . . . . . . . . . . . . . .
  . . . . . . . . . .sponsors

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Thank you very much
http//www.ysbl.york.ac.uk/alexei/
also program is available from
CCP4