Don't fffear the buccaneer Kevin Cowtan, York. ● Map simulation ⇨ A tool for building robust...
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Don't fffear the buccaneerKevin Cowtan, York.
● Map simulation⇨ A tool for building robust statistical methods
● 'Pirate'⇨ A new statistical phase improvement method
● 'Buccaneer'⇨ A new statistical chain tracing method
● Results⇨ And a diatribe about their irrelevance
The Royal SocietyYork Structural Biology Laboratory
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Map simulation
The Royal SocietyYork Structural Biology Laboratory
Refined modeldensity.
Targetnoisy map.
Simulatednoisy map.
Structurefactors
Known (reference) structure Unknown (work) structure
Phases
Scale factors
Phase errors
• Map simulation is a tool to generate problem specific statistical targets:
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Map simulation: Method
The Royal SocietyYork Structural Biology Laboratory
Low|E|
Med.|E|
High|E|
Med.resol.
Highresol.
Lowresol.
Low|E|
Med.|E|
High|E|
Med.resol.
Highresol.
Lowresol.
Transferring the errors:1. Classify the reflections from both structures by |E| and resol.
(Note: we use 225 bins, not 9!)
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Map simulation: Method
The Royal SocietyYork Structural Biology Laboratory
Low|E|
Med.|E|
High|E|
Med.resol.
Highresol.
Lowresol.
Low|E|
Med.|E|
High|E|
Med.resol.
Highresol.
Lowresol.
0.1, 0.00.0, 0.0
...
...
...
...
...0.9, 0.80.6, 0.4
...
...
Transferring the errors:2. Copy FOMs by bin from work structure to reference.
(We pick a random FOM from the same bin of the work structure for each reflection in the reference structure.)
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Map simulation: Method
The Royal SocietyYork Structural Biology Laboratory
P()
0
Transferring the errors:3. Simulate a phase error in accordance with the distribution
for that FOM:
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Map simulation: Method
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|E|2
Resolution
|E|2
Resolution
Transferring the scales:Rescale the reference data to match the work data, after
accounting for the difference in cell volumes.
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Map simulation: Method
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Result:
• Map calculated from simulated reference data has same statistical properties as work map.
Notes:
• Need reliable FOMs!
• Can potentially simulate HL coeffs too.
• Should bin FOMs for centric/acentric data separately (if data available).
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'Pirate': Rationale• Density modification history has been
dominated by the solvent mask in one form or another.
• Limitations:– What do we do with disordered protein?
– What do we do with ordered solvent?
– Need to know solvent content.
– What do we do for non-proteins?
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'Pirate': Method• Divide map into a multi-dimensional
continuum of states.
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e.g. Local mean and local variance classify map into:
●Electron sparse/dense●Disordered/ordered
Dense, ordered
Dense, disordered
Sparse, ordered
Sparse, disordered
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'Pirate': MethodCompare simulated and known map to obtain density distributions for each region, then apply these distributions to the unknown map.
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Reference structure: Work structure:
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'Pirate': Method• Obtain per-grid density probability distributions
– Also allows NCS, known density etc.
• Transform using equations of Bricogne (1992).– Similar to Terwilliger (1999).
– Map probability becomes phase probability distribution.
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Bricogne (1992) Proc. CCP4 Study WeekendBricogne (1997) Methods in Enzymology
R
I
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'Pirate': Method
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• Finally, combine new distribution with original HL coefficients, for new phases and maps.
• Gives final 'improved' phase probabilities.
R
I
R
I
X ABCD
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'Pirate': Method
The Royal SocietyYork Structural Biology Laboratory
Notes:• No solvent content required, since reference map is
pre-scaled to work map.
• Single step process (for now)
– No solvent mask -> no mask to refine.
• Should work for novel problems too (with related reference structure)
– e.g. No solvent, disordered domains, metaloproteins.
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'Buccaneer': MethodCompare simulated map and known model to obtain likelihood target, then search for this target in the unknown map.
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Reference structure: Work structure:
LLK
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'Buccaneer': Method• Compile statistics for reference map in 4A
sphere about C => LLK target.
The Royal SocietyYork Structural Biology Laboratory
4A sphere about Ca also used by 'CAPRA'Ioeger et al. (but different target function).
• Use mean/variance (in future histogram).
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'Buccaneer': MethodFind candidateC positionsusing LLK-fffearsearch.(~1 per 3 residues)
The Royal SocietyYork Structural Biology Laboratory
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'Buccaneer': MethodExtend fromcandidates using 2 residue lookahead withRamachandranrestraints.
(Same target-fn.but in real space)
Then ARP/wARP?
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Lookahead search c.f.Jones, Oldfield, Terwilliger, etc.
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ResultsProblem: “tuning” of one program to another.
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Ecorr
/ MPEw
/ m0
Phasing Ph.Impr.Ecorr
/ MPEw
/ m0
'dm'
'resolve'
'dm'
'resolve'
'mlphare'
'solve'
0.508 / 59.1 / 1.35
0.474 / 61.0 / 0.83
0.700 / 50.6 / 0.61
0.436 / 67.8 / 0.37
0.750 / 47.7 / 0.68
0.710 / 48.0 / 0.67
'resolve' version 2.0.5, with 'no build' optionin order to compare model-free phasing.
Statistics are: Ecorr
: E-map correlation;
MPEw: weighted Mean Phase Error;
m0: gradient of regression of cos() vs.
FOM
What other examples of “tuning” are present in this case?
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ResultsAfter 'solve', but with other tuning problems:
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Ecorr
/ MPEw
/ m0Ph.Impr.
'pirate' 1
'resolve'
'dm' 0.750 / 47.7 / 0.68
0.710 / 48.0 / 0.67
0.775 / 43.2 / 1.08
'pirate' 2
'pirate' 3
'pirate' 6
'pirate' 5
'pirate' 4
0.762 / 43.3 / 0.98
0.824 / 37.2 / 1.02
0.788 / 39.7 / 0.94
0.745 / 44.7 / 1.02
0.759 / 42.7 / 0.94
Reference structures
Beta-mannosidase (2003) StructureBoraston, Revett, Boraston, Nurizzo, Davies
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Results
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SAD 'dm'
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Results
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'resolve' 'pirate'
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ResultsOther cases:
– MIRAS:
• Commercial structure phased with MLPHARE.
• Results better than 'dm'.
– High resolution:
• RNAse phase extension to 1.5, 1.0A.
• Map improved (unlike 'dm') with appropriate reference structure.
• (But not as good a dual space methods: ACORN).
The Royal SocietyYork Structural Biology Laboratory
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Future• 'Pirate' available soon Q1 2004 (after tuning)
• 'Pirate' flexi-domain averaging Q3 2004
• 'Buccaneer' 2004?
Technology:
Both applications are extremely simple, built using Clipper libraries, less than 1000 lines of code each, less than 2 months development.
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Conclusions• Very simple but effective applications can be
built with improved statistical targets from map simulation calculations.
• Preliminary results on real data suggest this approach is competitive with the state-of-the-art, even at an early stage of development.
• Need reliable phase probability distributions (figures of merit).
The Royal SocietyYork Structural Biology Laboratory
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Acknowledgements
● G. Bricogne(Original probability transformation eqns.)
● T. Terwilliger(First implementation of statistical dm.)
● E. Dodson(Test data)
● Royal Society (KDC funding)