Ab initio methods: how/why do they work Ab i iti th d h / h d th - - PowerPoint PPT Presentation

Ab i iti th d h / h d th k Ab initio methods: how/why do they work

D.Svergun

Data analysis

Detector

Small Small-

• angle scattering in structural biology

angle scattering in structural biology

R l ti

Sh

2θ Sample Incident beam Wave vector k k=2π/λ

g I, relative

2 3

Scattering I( ) Resolution, nm: 3.1 1.6 1.0 0.8

Shape determination Rigid body

Solvent k, k=2π/λ Scattered beam, k1

l

1

curve I(s)

Missing Rigid body modelling

Radiation sources: X-ray tube (λ = 0.1 - 0.2 nm) Synchrotron (λ = 0.05 - 0.5 nm) Thermal neutrons (λ = 0.1 - 1 nm)

s, nm -1 2 4 6 8

EM

Complementary Complementary techniques techniques Oligomeric mixtures g fragments

Homology models Atomic models MS Distances Crystallography NMR h Bioinformatics

Hierarchical systems

Orientations Interfaces

Additional Additional information information

Biochemistry FRET AUC

Flexible systems

EPR

Major problem for biologists using SAS Major problem for biologists using SAS

• In the past, many biologists did

not believe that SAS yields more not believe that SAS yields more than the radius of gyration

• Now, an immensely grown

number of users are attracted by u b

• u

a a a d by new possibilities of SAS and they want rapid answers to more and more complicated Questions

• The users often have to

perform numerous cumbersome actions during the experiment and data analysis, to become each of the Answers

Now we shall go through the major steps required on the way

Step 1: know, which units are used Step 1: know, which units are used

The momentum transfer [q, Q, s, h, μ, κ …] = 4π sin(θ)/λ,

relative

3

Resolution, nm: 3.1 1.6 1.0 0.8

[q μ ] ( ) I(s)=I0*exp(-sRg/3), sRg <1.3 [ S k ] 2 i (θ)/λ

lg I,

1 2

Scattering curve I(s)

[s, S, k, … ] = 2 sin(θ)/λ I(s)=I0*exp(-2πsRg/3), sRg <1.3*2π

s, nm -1 2 4 6 8

GNOM or CRYSOL input: Angular units in the input file: 4*pi*sin(theta)/lambda [1/angstrom] (1) 4*pi*sin(theta)/lambda [1/nm] (2) 2 * sin(theta)/lambda [1/angstrom] (3) 2 sin(theta)/lambda [1/angstrom] (3) 2 * sin(theta)/lambda [1/nm] (4)

Scattering from dilute macromolecular Scattering from dilute macromolecular solutions (monodisperse systems) solutions (monodisperse systems)

dr sr r p s I

D

∫

= sin ) ( 4 ) ( π sr

∫

The scattering is proportional to that The scattering is proportional to that

• f a single particle averaged over all
• rientations,

which allows

• ne

to determine size, shape and internal structure of the particle at low (1-10 ) l ti nm) resolution.

Sample and buffer scattering Sample and buffer scattering

Overall parameters Overall parameters

Radius of gyration R (Guinier 1939)

) s R ) I( I(s)

g 2 2

3 1 exp( − ≅

Radius of gyration Rg (Guinier, 1939) Maximum size Dmax: p(r)=0 for r> Dmax Molecular mass (from I(0)) Excluded particle volume (Porod, 1952)

∫

∞

= =

2 2

) ( I(0)/Q; 2 V ds s I s Q π

The scattering is related to the shape The scattering is related to the shape (or lo resol tion str ct re) (or lo resol tion str ct re) (or low resolution structure) (or low resolution structure)

lg I(s), relative

• 1

Solid sphere

lg I(s), relative

• 1

lg I(s), relative

• 1

lg I(s), relative

• 1

lg I(s), relative

• 1
• 3
• 2

Hollow sphere

• 3
• 2
• 3
• 2
• 3
• 2
• 3
• 2
• 6
• 5
• 4
• 6
• 5
• 4
• 6
• 5
• 4
• 6
• 5
• 4

0 0 0 1 0 2 0 3 0 4 0 5

• 6
• 5
• 4

s, nm-1

0.0 0.1 0.2 0.3 0.4 0.5

Dumbbell

s, nm-1

0.0 0.1 0.2 0.3 0.4 0.5

s, nm-1

0.0 0.1 0.2 0.3 0.4 0.5

s, nm-1

0.0 0.1 0.2 0.3 0.4 0.5

s, nm-1

0.0 0.1 0.2 0.3 0.4 0.5

Long rod Flat disc

Shape determination: how? Shape determination: how? p

3D search model

M parameters

1D scattering

Trial-and-error Non linear

g data

Non-linear search

Lack of 3D information Lack of 3D information bl l d bl l d inevitably leads to inevitably leads to ambiguous interpretation, ambiguous interpretation, and additional information is and additional information is and additional information is and additional information is always required always required

Ab initio Ab initio methods methods

Advanced methods of SAS data l i l h i l h i analysis employ spherical harmonics (Stuhrmann, 1970) instead of Fourier t f ti transformations

The use of spherical harmonics

SAS i t it i I( ) <I( )> <{F [ ( )]}2> h F SAS intensity is I(s) = <I(s)>Ω = <{F [ρ(r)]}2>Ω, where F denotes the Fourier transform, <>Ω stands for the spherical average, and s=(s, Ω) is the scattering vector. Expanding ρ(r) in spherical harmonics p g ρ( ) p

) ( ) ( ) ( ω ρ ρ

lm lm l l m l

Y r

∑ ∑

− = ∞ =

= r

the scattering intensity is expressed as

I s A s

l l

( ) ( ) =

∞

∑ ∑

2

2 2

π I s A s

l m l lm

( ) ( ) =

= =−

∑ ∑

2 π

where the partial amplitudes Alm(s) are the Hankel transforms from the radial functions

A s i r j sr r dr

lm l lm l

( ) ( ) ( ) =

∞

∫

2

2

π ρ

and jl(sr) are the spherical Bessel functions.

Stuhrmann, H.B. Acta Cryst., A26 (1970) 297.

Structure of bacterial virus T7 Structure of bacterial virus T7

SAXS, 1982 SAXS, 1982 Cryo Cryo-

• EM, 2005

EM, 2005 Pro Pro-

• head

head Svergun, D.I., Feigin, L.A. & Schedrin, B.M. Svergun, D.I., Feigin, L.A. & Schedrin, B.M. (1982) (1982) Acta Cryst. Acta Cryst. A38 A38, 827 , 827 Agirrezabala, J. M. Agirrezabala, J. M. et al. et al. & Carrascosa J.L. (2005) & Carrascosa J.L. (2005) EMBO J. EMBO J. 24 24, 3820 , 3820 Mature virus Mature virus

Shape parameterization by spherical harmonics

Homogeneous particle Scattering density in spherical coordinates Homogeneous particle Scattering density in spherical coordinates (r,ω) = (r,θ,ϕ) may be described by the envelope function:

) ( , 1 ) ( ω F r ≤ ≤ ⎨ ⎧

r ρ

) ( ) ( , , ) ( ω ρ F r > ⎩ ⎨ ⎧ = r

Shape parameterization by a limited series of spherical harmonics:

F(ω) is an envelope function

∑ ∑

⋅ = ≅

L L

Y f F F ) ( ) ( ) (

l l l

ω ω ω

series of spherical harmonics:

envelope function

Ylm(ω) – orthogonal spherical harmonics, flm – parametrization coefficients,

Small-angle scattering intensity from the entire particle is

∑ ∑

= − =

≅

L

Y f F F ) ( ) ( ) (

l l m lm lm

ω ω ω

g g y p calculated as the sum of scattering from partial harmonics:

∑ ∑

L 2 2 l Stuhrmann, H. B. (1970) Z.

• Physik. Chem. Neue Folge 72,

177 198

∑ ∑

= − =

=

theor

s A s I

2 2

) ( 2 ) (

l l m lm

π

177-198. Svergun, D.I. et al. (1996) Acta

• Crystallogr. A52, 419-426.

H ti l

Shape parameterization by spherical harmonics

Homogeneous particle

f00 = + f + + +

r ρ

f00 A00(s) = f11 + + A11(s)

• F(ω) is an

r

f20 + +

• +

f22 +

• +

+…

( )

envelope function

A20(s) A22(s) +

Spatial resolution: , R – radius of an equivalent sphere.

) 1 ( π + = L R δ

p , q p Number of model parameters flm is (L+1)2. One can easily impose symmetry by selecting appropriate harmonics in the sum.

) 1 ( + L

One can easily impose symmetry by selecting appropriate harmonics in the sum. This significantly reduces the number of parameters describing F(ω) for a given L.

Program SASHA Program SASHA

Bead (dummy atoms) model Bead (dummy atoms) model

Vector of model parameters: A sphere of radius Dmax is filled by densely packed beads of radius r0<< Dmax ⎧ particle if 1 Position ( j ) = x( j ) = (phase assignments) Solvent Particle r0 Dmax ⎩ ⎨ ⎧ solvent if particle if 1

Number of model parameters M ≈ (Dmax / r0)3 ≈ 103 is too big for conventional minimization methods – Monte-Carlo like approaches are to be used

But: This model is able to describe rather complex describe rather complex shapes

Chacón, P. et al. (1998) Biophys. J. 74, 2760 2775 2r0 2760-2775. Svergun, D.I. (1999) Biophys. J. 76, 2879-2886 2r0

Dmax

Finding a global minimum Finding a global minimum

Pure Monte Carlo runs in a danger to be trapped into a Pure Monte Carlo runs in a danger to be trapped into a local minimum local minimum Solution: use a global minimization method like Solution: use a global minimization method like simulated annealing or genetic algorithm simulated annealing or genetic algorithm

Local and global search on the Great Wall Local and global search on the Great Wall

Local search always goes to a better Local search always goes to a better point and can thus be trapped in a local point and can thus be trapped in a local point and can thus be trapped in a local point and can thus be trapped in a local minimum minimum Pure Monte Pure Monte-

• Carlo search always goes to

Carlo search always goes to th l t l l i i ( t id th l t l l i i ( t id the closest local minimum (nature: rapid the closest local minimum (nature: rapid quenching and vitreous ice formation) quenching and vitreous ice formation) To get out of local minima, global search To get out of local minima, global search To get out of local minima, global search To get out of local minima, global search must be able to (sometimes) go to a must be able to (sometimes) go to a worse point worse point Slower annealing allows to search for a Slower annealing allows to search for a Slower annealing allows to search for a Slower annealing allows to search for a global minimum (nature: normal, e.g. global minimum (nature: normal, e.g. slow freezing of water and ice formation) slow freezing of water and ice formation)

Simulated annealing Simulated annealing

Aim: find a vector of M variables {x} minimizing a function f(x) 1. Start from a random configuration x at a “high” temperature T. 2. Make a small step (random modification of the configuration) x → x’ and 2. Make a small step (random modification of the configuration) x → x and compute the difference Δ = f(x’) - f(x). 3. If Δ < 0, accept the step; if Δ > 0, accept it with a probability e- Δ /T 4. Make another step from the old (if the previous step has been rejected) 4. Make another step from the old (if the previous step has been rejected)

• r from the new (if the step has been accepted) configuration.

5. Anneal the system at this temperature, i.e. repeat steps 2-4 “many” (say, 100M tries or 10M successful tries, whichever comes first) times, (say, 100M tries or 10M successful tries, whichever comes first) times, then decrease the temperature (T’ = cT, c<1). 6. Continue cooling the system until no improvement in f(x) is observed. Shape determination: M≈ 103 variables (e.g. 0 or 1 bead assignments in DAMMIN Rigid body methods: M≈ 101 variables (positional and rotational parameters Rigid body methods: M≈ 10 variables (positional and rotational parameters

• f the subunits)

f(x) is always (Discrepancy + Penalty)

Ab initio Ab initio program DAMMIN program DAMMIN

Using Using simulated simulated annealing, annealing, finds finds a a compact compact dummy dummy atoms atoms configuration configuration X X that that fits fits the the scattering scattering data data by by i i i i i i i i minimizing minimizing

) ( )] , ( ), ( [ ) (

exp 2

X P X s I s I X f α χ + =

where where χ is is the the discrepancy discrepancy between between the the experimental experimental and and calculated calculated curves, curves, P(X) P(X) is is the the penalty penalty to to ensure ensure compactness compactness and and connectivity, connectivity, α> 0 its its weight weight. .

compact compact p loose loose disconnected disconnected

Why/how do Why/how do ab initio ab initio methods work methods work

The 3D model is required not only to fit the data but also to fulfill (often stringent) physical and/or biochemical constrains

Why/how do Why/how do ab initio ab initio methods work methods work

The 3D model is required not only to fit the data but also to fulfill (often stringent) physical and/or biochemical constrains

A test A test ab initio ab initio shape determination run shape determination run

Program DAMMIN Slow mode Bovine serum albumin, molecular mass 66 kDa, no symmetry imposed

A test A test ab initio ab initio shape determination run shape determination run

Program DAMMIN Slow mode Bovine serum albumin: comparison of the ab initio model with the crystal structure of human serum albumin

DAMMIF, a fast DAMMIN DAMMIF, a fast DAMMIN

DAMMIF is a completely reimplemented DAMMIN written in object-oriented code

• About 25-40 times faster

than DAMMIN (in fast mode takes about 1 2 min mode, takes about 1-2 min

• n a PC)
• Employs adaptive search

volume

• Makes use of multiple

CPUs

Franke, D. & Svergun, D. I. (2009)

• J. Appl. Cryst. 42, 342–346

Limitations of shape determination Limitations of shape determination Limitations of shape determination Limitations of shape determination

Very low resolution

Very low resolution

Ambiguity of the models

Ambiguity of the models Accounts for a restricted portion of the data

lg I(s) 8 Resolution, nm 2.00 1.00 0.67 0.50 0.33 7

Shape

Atomic structure

How to construct ab initio

5 6

F

• ld

How to construct ab initio models accounting for higher resolution data?

s, nm-1 5 10 15

Ab initio Ab initio dummy residues model dummy residues model

Proteins

Proteins typically typically consist consist

• f
• f

folded folded polypeptide polypeptide chains chains composed composed of

• f amino

amino acid acid residues residues At a resolution

• f

0.5 nm a protein can be represented by an ensemble of K dummy residues Scattering from such a model centered at the Cα positions with coordinates { ri} Scattering from such a model is computed using the Debye (1915) formula. Starting from a random model, simulated annealing is employed similar to DAMMIN

Distribution of neighbors g

Excluded volume effects and local interactions lead to a characteristic distribution of nearest neighbors g around a given residue in a polypeptide chain

Number of neighbours 5 6 3 4 1 2 Shell radius, nm 0.2 0.4 0.6 0.8 1.0

GASBOR run on C subunit of V GASBOR run on C subunit of V-

• ATPase

ATPase

Starting from g a random “gas”

• f 401 dummy
• f 401 dummy

residues, fits the data by a the data by a locally chain- tibl compatible model

GASBOR run on C subunit of V GASBOR run on C subunit of V-

• ATPase

ATPase

Beads: Ambruster Beads: Ambruster et al. et al. (2004, June) (2004, June) FEBS Lett. 570, 119 , Cα trace: Drory et al. (2004 November) (2004, November), EMBO reports, 5, 1148

Benchmarking Benchmarking ab initio ab initio methods methods

log I relative

Envelope Envelope Bead model Bead model Dummy residues Dummy residues

log I, relative Experimental data Envelope model Bead model 2 Bead model Dummy residue model 1

1

5 10 s, nm-1

Comparison with the crystal Comparison with the crystal SASHA SASHA DAMMI N DAMMI N GASBOR GASBOR structure structure of lysozyme

• f lysozyme 1996

1996 1999 1999 2001 2001

Modular structure of a giant mucsle protein titin

Z M

I27 FNIII TK M5

Z

26 926 aa 1.2 μm 26 926 aa

N C

Z-disc I-band A-band H-zone Z1Z2 Z7 I1 I27 Ax TK M5 fold IG EF IG IG FN-III kinase IG method X NMR X NMR NMR X NMR

NMR data: Pastore lab; X-ray data: Wilmanns lab

• Z1Z2 includes two modules at the N

Z1Z2 includes two modules at the N-terminal of the Z terminal of the Z-disc of titin and disc of titin and

Solution structure of Z1Z2 Solution structure of Z1Z2-

• telethonin complex

telethonin complex

Z1Z2 includes two modules at the N Z1Z2 includes two modules at the N terminal of the Z terminal of the Z disc of titin and disc of titin and interacts with telethonin interacts with telethonin Shape of Z1Z2 and localization of the his-tag Cross-linking function

• f telethonin

Native Z1Z2 His-Z1Z2 Tele90-Z1Z2 Tele90 Z1Z2

Zou, P ., Gautel, M., Geerlof, M., Wilmanns, M., Koch, M.H.J. & Svergun, D.I. (2003)

• J. Biol. Chem. 278, 2636

Crystal structure of Z1Z2 Crystal structure of Z1Z2-

• telethonin complex

telethonin complex

~100 Å

Zou P ., Pinotsis N., Lange S., Song Y .H., Popov A., Mavridis I., Mayans O.M., Gautel M. & Wilmanns M. (2006) Nature 439, 229-33.

Shape analysis for multi Shape analysis for multi-

• component

component t i i l t i i l systems: principle systems: principle

One component, one scattering pattern: “normal” shape determination One component, one scattering pattern: “normal” shape determination

Chacón, P . et al. (1998) Biophys. J. 74, 2760-2775 Svergun, D.I. (1999) Biophys. J. 76, 2879-2886

Shape analysis for multi Shape analysis for multi-

• component

component t i i l t i i l systems: principle systems: principle

A+ B A B

Many components, many scattering patterns: shape and internal structure Many components, many scattering patterns: shape and internal structure

Svergun, D.I. (1999) Biophys. J. 76, 2879-2886 Svergun, D.I. & Nierhaus, K.H. (2000) J. Biol. Chem. 275, 14432-14439

EGC stator sub-complex of V-ATPase

EG+ C C subunit Ab initio shapes C subunit EG subunit Scattering from free subunits and their complex in solution complex in solution

3D map of the yeast V-ATPase by electron microscopy.

In solution, EG makes an L-shaped assembly with subunit-C. This model is supported by the EM showing three copies of EG, two of them linked by C. The data further indicate a conformational

py

Diepholz, M. et al. (2008) Structure 16, 1789-1798

t e ed by C e data u t e d cate a co

• at o a

change of EGC during regulatory assembly/disassembly.

Scattering from a multiphase particle Scattering from a multiphase particle Scattering from a multiphase particle Scattering from a multiphase particle

lg I, relative

11 0% D2O 40% D2O 55% D2O 10 75% D2O 100% D2O 8 9

s, nm-1

0.5 1.0 1.5 2.0 8

∑ ∑

2

∑ ∑

>

Δ Δ + Δ =

k j jk m i m j j j m j m

s I s I s I ) ( 2 ) ( ) ( ) (

2

ρ ρ ρ

Ab initio Ab initio multiphase modelling multiphase modelling

Start: random phase assignments within the search volume, no fit to the experimental data Finish: condensed multiphase model with minimum interfacial area fitting multiple data sets the experimental data fitting multiple data sets

Program MONSA, Svergun, D.I. (1999) Biophys. J. 76, 2879; Petoukhov, M.V. & Svergun, D. I. (2006) Eur. Biophys. J. 35, 567.

Ternary complex: Exportin Ternary complex: Exportin-

• t/Ran/tRNA

t/Ran/tRNA y p p y p p

Ran (structure known) Exportin-t t-RNA (structure known) Ran (structure known) Exportin t t RNA (structure known) (tentative homology model)

X-

• rays:

rays: ab initio ab initio overall shape

• verall shape

y p

lg I, relative

8 Ternary complex Ran tRNA Fits 6 7 0 5 1 0 1 5 2 0 5

s, nm-1

0.5 1.0 1.5 2.0

One X-ray scattering pattern from the ternary complex fitted by DAMMIN

Fukuhara, N., Fernandez, E., Ebert, J., Conti, E. & Svergun, D. I. (2004) J. Biol. Chem. 279, 2176

Scattering data from Exportin Scattering data from Exportin-

• t/Ran/tRNA

t/Ran/tRNA

X-

• ray scattering

ray scattering

• From Exportin

From Exportin-t, Ran, tRNA t, Ran, tRNA 3 curves 3 curves From Exportin From Exportin t, Ran, tRNA t, Ran, tRNA 3 curves 3 curves

Neutron scattering Neutron scattering

• Ternary complex with protonated Ran

Ternary complex with protonated Ran in 0, 40, 55, 75, 100% D in 0, 40, 55, 75, 100% D2O 5 curves 5 curves

• Ternary complex with deuterated Ran

Ternary complex with deuterated Ran y p y p in 0, 40, 55, 70, 100% D in 0, 40, 55, 70, 100% D2O 5 curves 5 curves

TOTAL TOTAL 13 curves 13 curves

Contrast variation: localization of tRNA Contrast variation: localization of tRNA

lg I, relative

8 Ternary complex Ran tRNA Fits

lg I, relative

6 7 11 0% D2O 40% D2O 55% D2O 75% D2O 100% D 0 5 1 0 1 5 2 0 5 9 10 100% D2O Fits

s, nm-1

0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 8

Three X ray and five neutron data

s, nm-1

Three X-ray and five neutron data sets fitted by MONSA

Specific deuteration: highlighting d Specific deuteration: highlighting d-

• Ran

Ran p g g g p g g g

lg I, relative

7 8 Ternary complex Ran tRNA Fits

lg I, relative

11 0% D2O 40% D2O

lg I, relative

6 7 10 55% D2O 75% D2O 100% D2O Fits

11 0% D2O 40% D2O 55% D2O 70% D O

s, nm-1

0.5 1.0 1.5 2.0 5 9

10 70% D2O 100% D2O Fits

, s, nm-1

0.5 1.0 1.5 2.0 8

9

Three X ray and ten neutron data

s, nm-1

0.5 1.0 1.5 2.0

Three X-ray and ten neutron data sets fitted by MONSA

Ternary complex: Exportin Ternary complex: Exportin-

• t/Ran/tRNA

t/Ran/tRNA y p p y p p

lg I, relative

8 Ternary complex Ran tRNA

lg I, relative

11 0% D2O 40% D O 6 7 tRNA Fits 9 10 40% D2O 55% D2O 75% D2O 100% D2O Fits

s, nm-1

0.5 1.0 1.5 2.0 5

s, nm-1

0.5 1.0 1.5 2.0 8 9

lg I, relative

11 0% D2O 40% D2O 55% D2O 10

70% D2O 100% D2O Fits

High resolution models of the components docked into the three-phase ab initio model of the l b d X d t tt i

s, nm-1

0.5 1.0 1.5 2.0 9

complex based on X-ray and neutron scattering from selectively deuterated particles

Shapes from recent projects at EMBL-HH

Domain and quaternary structure Complexes and assemblies Domain and quaternary structure Complexes and assemblies

Dcp1/Dcp2 complex S-layer proteins Toxin B α-synuclein oligomers She et al, Mol Cell (2008) Fagan et al Mol. Microbiol (2009) Albesa-Jové et al JMB (2010) Giehm et al PNAS USA (2011)

Structural transitions Flexible/transient systems

Src kinase Cytochrome/adrenodoxin Microbiol (2009) Complement factor H Bernado et al JMB (2008) Xu et al JACS (2008) Morgan et al NSMB (2011)

Ab i iti Ab i iti p f SAS p f SAS Ab initio Ab initio programs for SAS programs for SAS

• Genetic algorithm DALAI GA (Chacon et al., 1998, 2000)

Genetic algorithm DALAI GA (Chacon et al., 1998, 2000)

• Genetic algorithm DALAI_GA (Chacon et al., 1998, 2000)

Genetic algorithm DALAI_GA (Chacon et al., 1998, 2000)

• ‘Give

‘Give-

• n

n-

• take’ procedure SAXS3D (Bada et al., 2000)

take’ procedure SAXS3D (Bada et al., 2000)

• Spheres modeling program GA STRUCT (Heller et al., 2002)

Spheres modeling program GA STRUCT (Heller et al., 2002)

• Spheres modeling program GA_STRUCT (Heller et al., 2002)

Spheres modeling program GA_STRUCT (Heller et al., 2002)

• Envelope models: SASHA

Envelope models: SASHA(1)

(1) (Svergun et al., 1996)

(Svergun et al., 1996)

• Dummy atoms: DAMMIN

Dummy atoms: DAMMIN(1,4)

(1,4) & MONSA

& MONSA(1,2)

(1,2) (Svergun 1999)

(Svergun 1999)

• Dummy atoms: DAMMIN

Dummy atoms: DAMMIN(

) ( ) & MONSA

& MONSA(

) ( ) (Svergun, 1999)

(Svergun, 1999)

• Dummy residues: GASBOR

Dummy residues: GASBOR(1,3)

(1,3) (Petoukhov et al., 2001)

(Petoukhov et al., 2001)

(1) (1) Able to impose symmetry and anisometry constrains

Able to impose symmetry and anisometry constrains

( ) ( ) Able to impose symmetry and anisometry constrains

Able to impose symmetry and anisometry constrains

(2) (2) Multiphase inhomogeneous models

Multiphase inhomogeneous models

(3) (3) Accounts for higher resolution data

Accounts for higher resolution data

( ) ( ) Accounts for higher resolution data

Accounts for higher resolution data

(4) (4) DAMMIF is 30 times faster (D.Franke & D.Svergun, 2009)

DAMMIF is 30 times faster (D.Franke & D.Svergun, 2009)

Some words of caution Some words of caution

Or Always remember about ambiguity!

Shape determination of 5S RNA: a variety of Shape determination of 5S RNA: a variety of DAMMIN models yielding identical fits DAMMIN models yielding identical fits y g y g

Funari, S., Rapp, G., Perbandt, M., Dierks, K., Vallazza, M., Betzel, Ch., Erdmann, V. A. & Svergun, D. I. (2000) J. Biol. Chem. 275, 31283-31288.

Program Program SUPCOMB SUPCOMB – – a tool to align and conquer a tool to align and conquer

Aligns heterogeneous high

Aligns heterogeneous high-

• and low

and low-

• resolution models and

resolution models and provides a dissimilarity measure (NSD) provides a dissimilarity measure (NSD)

For shape determination allows one to find common

For shape determination allows one to find common

For shape determination, allows one to find common

For shape determination, allows one to find common features in a series of independent reconstructions features in a series of independent reconstructions

Kozin, M.B. & Svergun, D.I. (2001) J. Appl. Crystallogr. 34, 33-41

Automated analysis of multiple models Automated analysis of multiple models

1. Find a set of solutions starting from random initial models and superimpose all pairs of models with SUPCOMB

Automated analysis of multiple models Automated analysis of multiple models

superimpose all pairs of models with SUPCOMB. 2. Find the most probable model (which is on average least different from all the others) and align all the other models with this reference

• ne.

3. Remap all models onto a common grid to obtain the solution spread region and compute the spatial occupancy density of the grid points region and compute the spatial occupancy density of the grid points. 4. Reduce the spread region by rejecting knots with lowest occupancy to find the most populated volume 5. These steps are automatically done by a package called DAMAVER if you just put all multiple solutions in one directory

Program DAMAVER, Volkov & Svergun (2003) J. Appl. Crystallogr. 36, 860

5S RNA: ten shapes superimposed 5S RNA: ten shapes superimposed

Solution spread region Solution spread region

5S RNA: ten shapes superimposed 5S RNA: ten shapes superimposed

Most populated volume Most populated volume

5S RNA: final solution 5S RNA: final solution

The final model obtained within The final model obtained within the solution spread region the solution spread region

St bl l ti

Uniqueness of Uniqueness of ab initio ab initio analysis analysis

10

• 1

10

data SASHA DAMMIN

Stable solutions

10

• 1

10

data SASHA DAMMIN

cube cube

10

• 3

10

• 2

10 DAMMIN 10

• 3

10

• 2

10 0.0 0.2 0.4 0.6 0.8 1.0 10

• 4

s

0.0 0.2 0.4 0.6 0.8 1.0

s

Prism 1:2:4 Prism 1:2:4

I

data SASHA

cylinder 2:5 cylinder 2:5

Spread Spread Average NSD ≈ 0.5 Average NSD ≈ 0.5

10

10

10

DAMMIN

region Most region Most

0.0 0.1 0.2 0.3 0.4 10

s

Most probable volume Most probable volume

Fair stability Fair stability

cylinder 1:10 cylinder 1:10

10

I

data SASHA DAMMIN

Spread region Spread region

10

Most probable l Most probable l

0.0 0.1 0.2 0.3

s

Ring 1:3:1 Ring 1:3:1

volume volume Average NSD ≈ 0.9 Average NSD ≈ 0.9

10

10

I

data body 1 body 2

1

g

Spread region Spread region

10

10

3

1

Most probable Most probable

0.0 0.1 0.2 0.3

s

volume volume

Volkov, V .V . & Svergun, D.I. (2003) J. Appl. Crystallogr. 36, 860-864.

Poor stability Poor stability

Disk 5:1 Disk 5:1

10

10

data SASHA DAMMIN

Spread region Spread region

10

10

10

Most probable volume Most probable volume

0.0 0.1 0.2 0.3 10

s

Disk 10:1 Disk 10:1

Very long search may provide more accurate model Very long search may provide more accurate model

10

I

data SASHA DAMMIN

Spread region Spread region

10

g Most probable volume g Most probable volume

0.0 0.1 0.2 0.3

s

This structure can not be restored without use of additional information This structure can not be restored without use of additional information Average NSD > 1 Average NSD > 1

Use of symmetry Use of symmetry

Typical solution with P5 symmentry Typical solution with P5 symmentry Original body Original body Typical solution with no Typical solution with no Typical solution with no symmetry Typical solution with no symmetry Spread region Most probable volume Spread region Most probable volume

However: symmetry biases the results and must also be used with caution. Always run in P1 first! However: symmetry biases the results and must also be used with caution. Always run in P1 first!

Shape determination of V1 ATPase

P1 P3 P3, prolate

Svergun, D.I., Konrad, S., Huss, M., Koch, M.H.J., Wieczorek, H., Altendorf, K.- H., Volkov, V .V . & Grueber, G. (1998) Biochemistry 37, 17659-17663.

Progress in Progress in ab initio ab initio methods methods

2012 2012 1993 1993

And now let us awake for the practical work

M.Petoukhov,

D Franke: D.Franke:

Ab initio tutorial