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

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

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

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

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.

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

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

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

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

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