A practical introduction to quantum scattering theory, and ...
EMBO Practical Course on Solution Scattering from ...€¦ · EMBO Practical Course on Solution...
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EMBO Practical Course on Solution Scattering from Biological Macromolecules
D R id M d lD R id M d lDummy Residues ModelDummy Residues ModelProteins typically consist of folded polypeptide• Proteins typically consist of folded polypeptidechains composed of amino acid residues
• At a resolution of 0 5 nm each amino acid can beAt a resolution of 0.5 nm each amino acid can berepresented as one entity (dummy residue)
• In GASBOR a protein is represented by anbl f K DR thensemble of K DRs those are
– IdenticalHave no ordinal– Have no ordinalnumber
– For simplicity areFor simplicity arecentered at the Cαpositions
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EMBO Practical Course on Solution Scattering from Biological Macromolecules
DR M d lli GASBORDR M d lli GASBORDR Modelling: GASBORDR Modelling: GASBOR• Finds coordinates {ri}
of K DRs within the sphericalh lsearch volume
• Scattering is computed usingth D b (1915) f lthe Debye (1915) formula
( ) ( ) ( )∑∑=K K
ijjiDR
srsgsgsI
sin
• Requires polypeptide chain-
( ) ( ) ( )∑∑= =i j ij
jiDR sr1 1
= < … … >q p yp p
compatible arrangement ofDRs
D.I. Svergun, M.V. Petoukhov, & M.H.J. Koch (2001) Biophys. J. 80, 2946-53
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EMBO Practical Course on Solution Scattering from Biological Macromolecules
GASBOR R t i tGASBOR R t i tGASBOR RestraintsGASBOR RestraintsE l d d l ff t d l l i t ti l d tExcluded volume effects and local interactions lead to acharacteristic distribution of nearest neighbors around agiven residue in a polypeptide chain
Number of neighbours6
4
5
2
3
0 2 0 4 0 6 0 8 1 00
1
Shell radius, nm
0.2 0.4 0.6 0.8 1.0
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EMBO Practical Course on Solution Scattering from Biological Macromolecules
DR modelling program GASBORDR modelling program GASBORDR modelling program GASBORDR modelling program GASBOR
searches for a chain-like arrangement of dummysearches for a chain like arrangement of dummy residues fitting the scattering data by minimizing
f (X) = χ2 + Σα P (X)
I, rel. units 2.0 p(r), rel. units
f (X) = χ + ΣαiPi(X)
100
1000
experiment calc. from p(r)
1.0
1.5
L t ti l ti
0 0 0 5 1 0 1 5 2 01
10
0 5 10 150.0
0.5 DmaxLong computational timefor large proteins0.0 0.5 1.0 1.5 2.0s, nm-1
• Symmetry can be taken into account; groups supported:
0 5 10 15 distance r, nm
y y g p ppPn, Pn2 (n=2..19), P23, P432 and icosahedral symmetry
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EMBO Practical Course on Solution Scattering from Biological Macromolecules
GASBOR SGASBOR SGASBOR SummaryGASBOR Summary• Task: Searches for a chain like arrangement of dummy• Task: Searches for a chain-like arrangement of dummy
residues fitting the scattering data.• Parameters: 3D coordinates of DRs describing CαParameters: 3D coordinates of DRs describing Cα
positions.• Objects: Applicable for polypeptide chains (i.e. proteins
and their assemblies) with K ≲ 5000.• Capabilities: Fits the scattering curves at higher angles.
Takes into account symmetry and anisometry ReciprocalTakes into account symmetry and anisometry. Reciprocaland real space fitting options.
• Limitations: Fits only SAXS data and applicable forLimitations: Fits only SAXS data and applicable forproteins only. CPU time is quadratically proportional to K.
• Theoretical intensity: computed using the Debyeformula.
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GASBORGASBOR ll
EMBO Practical Course on Solution Scattering from Biological Macromolecules
GASBOR GASBOR examplesexamples
• Neocarzinostatin, 113 AA• Catalase, tetramaer, P222, 501AA per , , , p
monomer
• supcomb 1NOA.PDB test01.pdb -e --superposition=backbone
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EMBO Practical Course on Solution Scattering from Biological Macromolecules
n: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Fib(n): 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987
Δρ=0.03 e/A3
Width=3A
ρ=0.334 e/A3
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EMBO Practical Course on Solution Scattering from Biological Macromolecules
MONSA (multiphase modelling)MONSA (multiphase modelling)MONSA (multiphase modelling)MONSA (multiphase modelling)
DAMMIN/F shape determination
• One can differentiate between distinct partsbetween distinct parts of the particle
• Several curves are requiredrequired
• Assuming the same arrangement of the
t i diff tparts in different samples
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EMBO Practical Course on Solution Scattering from Biological Macromolecules
MONSA (multiphase modelling)MONSA (multiphase modelling)MONSA (multiphase modelling)MONSA (multiphase modelling)
1 h 1 t f l ti l• 1 phase = 1 component of a complex particle• For each phase, Rg, V and its scattering curve can be given• For each curve, contrast of each phase are specified , p p
contrast variation and / or use ofand / or use of partial constructs
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C 1C 1 t it i RNARNA ll
EMBO Practical Course on Solution Scattering from Biological Macromolecules
Case1: Case1: proteinprotein--RNA RNA complexcomplex
252 AA protein (two domains)
67 nucleotides RNA
Three curves in total:
Free RNA
Complex
Free protein