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Interactive fitting of high resolution modelsinto low resolution maps.
Last developments in the UROX software //http://mem.ibs.fr/UROX
Xavier Siebert and Jorge Navaza
Methods in Electron MicroscopyInstitut de Biologie Structurale
CNRS, Grenoble, France
Leiden, May 16, 2008
Fitting high resolution models . . .
◮ XRay crystallography
◮ need crystals◮ hard for large complexes
◮ NMR
◮ hard > 50kDa◮ many peaks◮ broader peaks
. . . into Electron Microscopy maps
Rotavirus, 25 Å (Jean Lepault)
. . . or Small Angle Scattering envelopes
Methods for Fitting
◮ “by hand”, with a graphics software◮ subjective (Wang et al. 1992 ; Stewart et al. 1993)
◮ with a fitting algorithm◮ real space : 3SOM, ADP_EM, CHIMERA, DOCKEM,
EMFIT, FOLDHUNTER, MOLREP, SITUS◮ reciprocal space : COAN, URO, UROX
◮ “force feedback 3D devices” : SENSITUS
Fitting in real space or reciprocal space ?
◮ minimize mismatch / maximize correlation (Q = 1 − CC2)◮ . . . in real space : between densities
Q =
∫
|ρem(r) − λρmod(r)|2d3r∫
|ρem(r)|2d3r
◮ . . . in reciprocal space : between Fourier coefficients
Q =
∫
|F em(s) − λF mod(s)|2d3s∫
|F em(s)|2d3s
◮ equivalent formulations (Parseval)
Reciprocal-space fitting with UROX
Application of UROX : Rotavirus (J. Virol, March 2008)Fitting in the whole reconstruction, using symmetry
Application of UROX : RotavirusChannel shrinks (right), inhibiting transcription
Reciprocal-space formulation with symmetry
◮ Goal : maximize correlation map - models:
CC =
∫
F em(s)F mod(s)d3s√
∫
|F em(s)|2d3s√
∫
|F mod(s)|2d3s. (1)
◮ where F mod are functions of the positional variables of theindependent molecules :
F mod(s) =∑
m∈M
∑
g∈G
fm(sMgRm) exp[2πis(MgXm + Tg)] , (2)
◮ m = one of the M independent molecules, located at theposition Xm in the orientation Rm with respect to areference position
◮ g = symmetry operator represented by the translation Tg
and the rotation Mg.
UROX design
◮ core calculations : Fortran77 code (adapted from URO)◮ graphical libraries : VTK (Visualization Toolkit)◮ Python wrapper
◮ Tkinter : graphical user interface◮ F2PY : import fortran from python
VTK (Visualization Toolkit) www.vtk.org
◮ powerful libraries for medical and scientific applications
Why reciprocal space ?
Pros:
1. speed allows real-time calculations
2. choose fitting resolution without extra computations
3. use whole EM reconstruction (no masking)
4. symmetry (if any) incorporated in the formulation
Cons:◮ hard to impose real-space restrains
Why reciprocal space ?
Pros:
1. speed allows real-time calculations
2. choose fitting resolution without extra computations
3. use whole EM reconstruction (no masking)
4. symmetry (if any) incorporated in the formulation
Cons:◮ hard to impose real-space restrains
Why reciprocal space ?
Pros:
1. speed allows real-time calculations
2. choose fitting resolution without extra computations
3. use whole EM reconstruction (no masking)
4. symmetry (if any) incorporated in the formulation
Cons:◮ hard to impose real-space restrains
Why reciprocal space ?
Pros:
1. speed allows real-time calculations
2. choose fitting resolution without extra computations
3. use whole EM reconstruction (no masking)
4. symmetry (if any) incorporated in the formulation
Cons:◮ hard to impose real-space restrains
Why reciprocal space ?
Pros:
1. speed allows real-time calculations
2. choose fitting resolution without extra computations
3. use whole EM reconstruction (no masking)
4. symmetry (if any) incorporated in the formulation
Cons:◮ hard to impose real-space restrains
1. Speed of UROXInteractive graphics . . .
◮ fast calculation of correlation coefficient (CC):◮ 10−7 s / symmetry operation / Fourier coefficient
symmetry resol # coeff timeGroEl 14 30 Å ≈ 5000 3.5 ms
DLP (Rotavirus) 60 20 Å ≈ 650,000 4 s◮ interactive graphics
◮ CC computed in real-time as a model is moved in the map◮ speed up
◮ recuperate asymmetric unit in reciprocal space◮ decimate Fourier coefficients (only 6N unknowns !)
1. Speed of UROXInteractive graphics . . .
◮ fast calculation of correlation coefficient (CC):◮ 10−7 s / symmetry operation / Fourier coefficient
symmetry resol # coeff timeGroEl 14 30 Å ≈ 5000 3.5 ms
DLP (Rotavirus) 60 20 Å ≈ 650,000 4 s◮ interactive graphics
◮ CC computed in real-time as a model is moved in the map◮ speed up
◮ recuperate asymmetric unit in reciprocal space◮ decimate Fourier coefficients (only 6N unknowns !)
1. Speed of UROXInteractive graphics . . .
◮ fast calculation of correlation coefficient (CC):◮ 10−7 s / symmetry operation / Fourier coefficient
symmetry resol # coeff timeGroEl 14 30 Å ≈ 5000 3.5 ms
DLP (Rotavirus) 60 20 Å ≈ 650,000 4 s◮ interactive graphics
◮ CC computed in real-time as a model is moved in the map◮ speed up
◮ recuperate asymmetric unit in reciprocal space◮ decimate Fourier coefficients (only 6N unknowns !)
1. Speed of UROXInteractive graphics . . .
◮ fast calculation of correlation coefficient (CC):◮ 10−7 s / symmetry operation / Fourier coefficient
symmetry resol # coeff timeGroEl 14 30 Å ≈ 5000 3.5 ms
DLP (Rotavirus) 60 20 Å ≈ 650,000 4 s◮ interactive graphics
◮ CC computed in real-time as a model is moved in the map◮ speed up
◮ recuperate asymmetric unit in reciprocal space◮ decimate Fourier coefficients (only 6N unknowns !)
1. Speed of UROXInteractive graphics . . .
◮ fast calculation of correlation coefficient (CC):◮ 10−7 s / symmetry operation / Fourier coefficient
symmetry resol # coeff timeGroEl 14 30 Å ≈ 5000 3.5 ms
DLP (Rotavirus) 60 20 Å ≈ 650,000 4 s◮ interactive graphics
◮ CC computed in real-time as a model is moved in the map◮ speed up
◮ recuperate asymmetric unit in reciprocal space◮ decimate Fourier coefficients (only 6N unknowns !)
1. Speed of UROXInteractive graphics . . .
◮ fast calculation of correlation coefficient (CC):◮ 10−7 s / symmetry operation / Fourier coefficient
symmetry resol # coeff timeGroEl 14 30 Å ≈ 5000 3.5 ms
DLP (Rotavirus) 60 20 Å ≈ 650,000 4 s◮ interactive graphics
◮ CC computed in real-time as a model is moved in the map◮ speed up
◮ recuperate asymmetric unit in reciprocal space◮ decimate Fourier coefficients (only 6N unknowns !)
1. Speed of UROXInteractive graphics . . .
◮ fast calculation of correlation coefficient (CC):◮ 10−7 s / symmetry operation / Fourier coefficient
symmetry resol # coeff timeGroEl 14 30 Å ≈ 5000 3.5 ms
DLP (Rotavirus) 60 20 Å ≈ 650,000 4 s◮ interactive graphics
◮ CC computed in real-time as a model is moved in the map◮ speed up
◮ recuperate asymmetric unit in reciprocal space◮ decimate Fourier coefficients (only 6N unknowns !)
1. Speed of UROXInteractive graphics . . .
◮ fast calculation of correlation coefficient (CC):◮ 10−7 s / symmetry operation / Fourier coefficient
symmetry resol # coeff timeGroEl 14 30 Å ≈ 5000 3.5 ms
DLP (Rotavirus) 60 20 Å ≈ 650,000 4 s◮ interactive graphics
◮ CC computed in real-time as a model is moved in the map◮ speed up
◮ recuperate asymmetric unit in reciprocal space◮ decimate Fourier coefficients (only 6N unknowns !)
1. Speed of UROXInteractive graphics . . .
◮ fast calculation of correlation coefficient (CC):◮ 10−7 s / symmetry operation / Fourier coefficient
symmetry resol # coeff timeGroEl 14 30 Å ≈ 5000 3.5 ms
DLP (Rotavirus) 60 20 Å ≈ 650,000 4 s◮ interactive graphics
◮ CC computed in real-time as a model is moved in the map◮ speed up
◮ recuperate asymmetric unit in reciprocal space◮ decimate Fourier coefficients (only 6N unknowns !)
1. Speed of UROXSpeedup Graphics (for oldish graphics cards like mine . . . )
◮ VTK decimation (wireframe mode)
1. Speed of UROXSpeedup Graphics (for oldish graphics cards like mine . . . )
◮ VTK decimation (surface mode)
1. Speed of UROXSpeedup Graphics
◮ VTK BoxWidget◮ Analyse local parts of the map (and speed up)
2. Change fitting resolutionCorrelation profile at 1
20 Å−1
-10
0
10
20
30
40
50
60
70
80
-40 -20 0 20 40 60 80 100
CC
Z [Angstroms]
20A
2. Change fitting resolutionCorrelation profile at 1
40 Å−1
-10
0
10
20
30
40
50
60
70
80
90
100
-40 -20 0 20 40 60 80 100
CC
Z [Angstroms]
40A
2. Change fitting resolutionCorrelation profile at 1
60 Å−1
-20
0
20
40
60
80
100
-40 -20 0 20 40 60 80 100
CC
Z [Angstroms]
60A
2. Change fitting resolutionStrategy
◮ to avoid local extrema :1. low resolution2. high resolution
◮ two modes :◮ interactive with least-squares optimization◮ exhaustive 3D or 6D searches
3. and 4. Use whole EM map and symmetryIllustrated by a benchmark comparison of several fitting softwares
◮ test case : GroEl (cryo-stain, Dubochet, JSB 2002)◮ D7 symmetry
3. and 4. - Benchmark : GroElWarning : subject to my mishandling of other people’s softwares
3. and 4. - Benchmark : GroElAnalysis of Benchmark for other softwares
◮ most softwares struggle because of "extra" density◮ alternative : mask around putative solution (but bias . . . )
◮ in that case most softwares find the solution
3. and 4. - Benchmark : GroElAnalysis of Benchmark for UROX (exhaustive search mode)
◮ without symmetry (C1) : difficult (requires tweaking)◮ with symmetry (D7) : easy (10 min)◮ conclusions :
◮ symmetry matters, no mask necessary◮ could use interactive mode instead of exhaustive search
Other features of UROX
◮ refine electron microscope magnification (5% error)
Latest developments (UROX 2.0)
◮ (re-writing of the Python classes . . . )◮ flexible fitting : normal modes◮ fit map in map◮ applications to tomography
UROX 2.0 - flexible fittingNormal modes (with K. Suhre and Y-H. Sanejouand)
◮ low frequency motion of proteins◮ harmonic approximation
rj(t) = r0j +
∑
k
Ajkαkcos(ωk t + φk ) (3)
◮ use with care (will always give better answer ! )
UROX 2.0 - fit map in map
UROX 2.0 - Tomography and missing wedgePresentation of the problem
UROX 2.0 - Tomography and missing wedgeVisualize the Fourier transform (and select reflections)
UROX 2.0 - Tomography and missing wedge
◮ Detect missing wedge◮ remove it from fitting (don’t align missing wedges !)
Thank you
. The Organizers . . .
. Jorge Navaza (IBS, Grenoble)
. Jean Lepault and Sonia Libersou (LVMS, Gif-sur-Yvette)
. Karsten Suhre (Neuherberg, Germany)
. Yves-Henri Sanejouand (ENS, Lyon)
. Leandro F. Estrozi (EMBL, Grenoble)
. Stefano Trapani (CBS, Montpellier)
. James Conway (Pittsburgh, USA)
. Irina Gutsche and Ambroise Desfosses (EMBL, Grenoble)
+ http://mem.ibs.fr/UROX
Error EstimatesMy map has a resolution of x Å. What is the error on the fit ?
◮ in UROX:1. R-factor ↔ quality of the map
R =
∑
h ||F emh | − |F mod
h ||∑
h |F emh |
2. Q = quadratic misfit
◮ rule of thumb : 10% resolution (Rossmann, Acta Crys. 2001)
◮ empirically : VP6 of the rotavirus (25 Å map)◮ fit with a trimer◮ fit with 3 monomers◮ RMSD (trimer, 3 monomers) ≈ 3 Å
Error Estimate by Least SquaresBorel p. 204
◮ let us suppose that the errors are distributed as a gaussian:
P(ǫ) =1
σ√
2πexp(− ǫ2
2σ2 ) (4)
◮ if σ is the same for all N reflections :
P({F modH , F em
H , σ}) = (1
σ√
2π)N exp(−
∑
H
|F emH − F mod
H |22σ2 ) (5)
σ ≈√
Qmin
N − M(6)