norbert kučerka

Norbert Kučerka

Frank Laboratory of Neutron Physicsat Joint Institute for Nuclear Research in Dubna

andDepartment of Physical Chemistry of Drugs

Faculty of Pharmacy at Comenius University in Bratislava

Экспериментальные методы молекулярной биофизикиМосковский физико-технический институт, Долгопрудный, Октябрь 26, 2020

Sources and Properties of X-rays and Neutrons

Principles of Small Angle Scattering

Model Independent Analysis of Small Angle Scattering

Small Angle Scattering Form Factors

Examples of Small Angle Scattering from Biomembranes

Beyond Scattering Experiments

• 1895 – Wilhelm Röntgen – discovery of X-rays

• 1903 – Antoine H. Becquerel & Pierre Curie & Maria Skłodowska-Curie – radiation phenomena

• 1917 – Ernest Rutherford – splitting the atom in a nuclear reaction

• 1932 – James Chadwick - discovery of neutron

• 1932 – John Cockcroft & Ernest Walton – controlled split of nucleus

• 1933 – Leó Szilárd – the idea of nuclear chain reaction

• 1937 – Glenn T. Seaborg – concept of nuclear spallation

• 1942 – Enrico Fermi – the first artificial nuclear reactor Chicago Pile-1

• 1947 – Elder, Gurewitsch, Langmuir and Pollock – observation of synchrotron radiation

• 1947-1993 & 1957 – National Research eXperimental & National Research Universal reactors

• 1950-1954 – Ernest O. Lawrence – the first spallation source Materials Testing Accelerator

• 1955 – Dimitry I. Blokhintsev – the idea of pulsed reactor

• 1960-1968-2001 – Ilya M. Frank & Fyodor L. Shapiro – the pulsed reactor IBR, IBR-30

• 1961 – Synchrotron Ultraviolet Radiation Facility at NIST – the first generation synchrotron

• 1970 – Synchrotron Radiation Source at Daresbury, UK – the second generation: dedicated source

• 1984-2006/2010-2037 – IBR-2, IBR-2M

• 1994 – European Synchrotron Radiation Facility – the third generation: optimized for brightness

• 2006-present – Spallation Neutron Source operational

• 2017-future – X-ray Free Electron Laser – the fourth generation synchrotron

• 2019-future – European Spallation Source constructing

Historical Overview

ЭММБ - МФТИ p.4

X-ray(1895) Sources Advancements

• Decelerating electron

• Bremsstrahlung radiation

• K-shell emission


SEALED TUBE

SYNCHROTRON

• Accelerating electron

Neutrons(1932) through Fission(1933) vs. Spallation(1937)

• fissile material required

• low energy needed

• low efficiency outcome

• no “dangerous goods”

• high energy particles needed

• high efficiency outcome


Neutron Sources based on Reactors(1942) vs. Accelerators(1951)

Continuous vs. Pulsed

National Research Universal (1957) reactor at Chalk River, ON

Spallation Neutron Source at Oak Ridge, TN (2006)

Inefficient use of neutrons produced in stationary reactors due to

• monochromators (acceptance~1%)

• choppers in Time-of-Flight methods

Complex systems at spallation sources


Idea of IBR (Импульсный Быстрый Реактор) in 1955

Institute of Physics and Power Engineering in Obninsk, Russia

The idea of the pulsed fast reactor of neutrons belongs to russian scientist Dimitry Ivanovich Blokhintsev

“Why not fix a part of the reactor active zone on a rim of the disk so that at each revolution this part passes near the stationary zone and creates a supercritical mass for a short time?”


Frank Laboratory of Neutron Physics in 1956-1960

1958 – Nobel Prize in physics toI.M.Frank and I.Ye.Tamm for a theoretical explanation of the Vavilov-Cherenkov radiation

World’s first reactor of a new type built in 3 years at the FLNPdirected by Nobel Laureate Ilya Mikhailovich Frank and under the guidance of Fyodor Lvovich Shapiro

• June 23, 1960 - start-up

• operation power of 1kW

• upgraded to 6kW


High Flux Pulsed Reactor IBR(1960)-2M(2010)

Neutron Sources Around the World

Report of a technical meeting held in Vienna, 18–21 May 2004 , IAEA-TECDOC-1439 (2005)


Advantages of Neutrons

• Charge:

• Magnetic Moment:

• Scattering Power:

==> deep penetration into matter

==> the world smallest magnetometer

==> sensitivity to light elements

==> sensitivity to isotope exchange


What Neutrons Can Do

Structure

C.G. Shull - The Nobel Prize in Physics 1994 - B.N. Brockhouse

Dynamics

“It might well be said that, if the neutron did not exist, it would need to be invented!”


- radiation (e.g. neutrons, X-rays, light) is elastically scattered by a sample and the resulting scattering pattern is analysed to provide information about the size, shape and location of some components of the sample

- Q range is usually between 0.003 and 0.3 Å-1 – providing a wide range of length scales (~10 to 1000 Å)

- powerful tool for investigating the average structure of the entire ensemble of particles in solution (biologically relevant environment)

- orientation of the studied structures is either isotropic or poorly ordered

- type of the sample, sample environment and the information that can ultimately be obtained depend on the nature of the radiation, however different radiations often provide complementary results

Common Features of Small Angle Scattering (SAS)


Scattered intensity is proportional to

“the square of the difference between scattering length density of studied

material and medium”

0 20 40 60 80 100-2.0

0.0

2.0

4.0

6.0

8.0-CD

2-

-CH2-

phospholipid

protein

water solution

RNA

DNA

deuterated RNA

deuterated protein

D2O / (D

2O + H

2O) [%]

Ne

utr

on

Sca

tte

rin

g L

en

gth

De

nsity

[10

-6xÅ

-2]

low contrast

2 ways to increase contrast

Neutron contrast variation can be done without changing the chemical properties of the system, because the neutron scattering lengths of isotopes can be very different.

Small Angle Neutron Scattering


Two ways to get small scattering vectors:

1.)

2.)

1.) large wavelengths

q =q = ks – ki

Scattering vector, q

ki

ks

qq

ki

==q||q

q R (detector cell)

D (sample-to-detector)

2DR

2θsin ~

Scattering Principles – Geometry

2θsin

λ4πq|| ==q

1.)

2.) small angles

λ

For l = 5.2 Å and qmin~ 0.28o, qmin ~ 0.006 Å-1.

Max. attainable length scale = 2p/qmin ~ 1000 Å.

near-source end

near-sample end

Scattering Principles – Triple Axis Spectrometer


120

100

80

60

40

20

0

120100806040200

-0.3 -0.2 -0.1 0.0

-0.2

-0.1

0.0

0.1

0.2

4.5

4.0

3.5

3.0

2.5

2.0

1.5

For l = 8 Å and qmin~ 0.25o, qmin ~ 0.003 Å-1.

Max. attainable length scale = 2p/qmin ~ 2000 Å.

Velocity

Selector

Neutron

Guide

2-D

Detector

Sample

table

circularly

averaged

into 1-D

102

2

4

103

2

4

I(q)

3 4 5 6 7 8 9

0.12

q

Neutron Beam

from Reactor

q =4p

lsin

q

2

Scattering Principles – 2D SANS Instrument


Scattering Principles – TOF SANS Instrument


Two ways to vary scattering vector:

1.) = TAS

2.) = TOF

2θsin

λ4πq|| ==q

through angles θ

through wavelengths λ

Scattering Principles – YuMO Instrument


http://flnph.jinr.ru/en/facilities/ibr-2/instruments/yumo

q

Wo

measured intensity at q (or q)

Im(q) = IF · Wo · e · T ·

Differential

cross-section

Flux Solid

angleDetector

efficiency Sample

transmission

ds

dW( )v ·A ·t

Beam area

on the sample

Path lengthDifferential

cross-section

number of neutrons scattered per second into a solid angle dW with the final energy between E and E+dE

neutron flux of the incident beam • dWdE

d2s(W,E)dWdE

=

For (quasi-)Elastic Scattering we assume no energy transfer

0

ds

dW=

d2sdWdE

dEnumber of neutrons scattered per second into dW

neutron flux of the incident beam • dW=

[time-1area-1]

[time-1]

[area]

Differential

cross-section

Scattering Principles – SAS Intensity


( )2

i

rqi

i

i j

rrqi

jiiji ebebb

dΩ

dσ

−==

Sρ)rρ()rΔρ( −=

rp

roVp

V

N particlesR

O

x

( )2

N

k i

xRqi

iVikeb

V

1)

dΩ

dσ(

+=

;dVe)xΔρ(eV

1)

dΩ

dσ(

2N

k

P

xqiRqi

Vk

=

)q)P(qS(V

N)

dΩ

dσ( V

=

Inter-particle structure factor

square of amplitude of (intra-)particle form factor

== 2

P

xqi2 |dV)exΔρ(||)qF(||)qP(|

orientational

average

SAS Data Factorization


2rqi

V dVe)rΔρ(V

N)

dΩ

dσ(

=

22

P

2

V ...2

)rq(-1ΔρV

V

NdV)rqcos(Δρ

V

N)

dΩ

dσ( +

−=

Assume a centro-symmetric particle with homogeneous ρ

;...3

Rq1VΔρ

V

N)

dΩ

dσ(

2

G22

P

2

V

+−=

(dilute system: S(q)=1)

Interpretation of Slopes

Decay of the scattering function depends on

the system’s overall structure (dimensionality)

cylinder

disk

;q~)dΩ

dσ( m-

V

m=1 - cylinders

m=2 - disks, lamellae

m=3 - fractals

m=4 - sharp interfaces

Model-Independent Analysis


...3

Rq)log(Ilog(I(q))

2

sphereG,2

0 +−=

...2

RqAI(q))log(q

2

cylinderG,2 +−=

...RqBI(q))log(q 2

lamellaG,

22 +−=

Radius of Gyration corresponds

to the “scattering size” of object

(substitute “scattering amplitude” for “mass”)

Modified Guinier Plots


Select a model for

possible structure

of the aggregates

Fit the experimental

data using the

selected model

(Fix the values of any

“known” physical

parameters - as

many as possible)

Is it a

good fit

? No

Change

the model

Yes

A Possible

Structure

Model-Based Analysis


10-2

10-1

100

101

102

103

104

I (a

rbitra

ry u

nit)

4 6 8

0.012 4 6 8

0.12

q (Å-1

)

10 oC

45 oC

10 oC

PathOblate shells: a=180 Å, b=62 Å

Spherical shells: R=133 Å, p= 0.15

Bilayer disks: R=156 Å, L= 45 Å

EXAMPLE:Bicelles forming mixture (DMPC, DHPC, and DMPG in D2O at the total lipid concentration of 0.1 wt.%)

Model-Based Analysis


Since spheres are isotropic, there

is no need to do orientational

average

r( r )·e-iq · r drP(q) = 1

Vsphere vsphere

2

2

= e-iqr·cosq r2 sinq dj dq dr1

Vsphere

2

2

r= 0

r= R

q= 0

q = p

j= 0

j= 2p

= [sin(qR) - qR·cos(qR)]29

(qR)6

10-5

10-3

10-1

101

arb

itra

ry u

nit

6 8

0.012 4 6 8

0.12

q, Å-1

R= 100 Å

Dr = 1x10-6 Å-2

f= 0.1

ds

dW( )v = (rsphere – ro) · Vsphere· P( q )

N

V

22

=fsphereVsphereDr2 [sin(qR) - qR·cos(qR)]2

9

(qR)6

rq

j

Scattering Form Factors – Spheres


Common form factors of particulate systems

Cylinders

(radius: R

length: L)

Spherical shells

(outer radius: R1

inner radius: R2)

Morphologies P(q)

Triaxial ellipsoids

(semiaxes: a,b,c)

Remarks

Spheres

(radius :R) [sin(qR) - qR·cos(qR)]2 =Asph(qR)9

(qR)62

(R13 – R2

3)2

[R13·Asph(qR1)– R2

3·Asph(qR2)]2

Asph[q a2 cos2(px/2) + b2sin2(px/2)(1-y2)1 + c2y2 ] dx dy0 0

1 12 • Integration of

x and y are for

orientational

average.

• J1(x) is the

first kind

Bessel

function of

order 1

0

1J1

2[qR 1-x2 ]4

[qR 1-x2 ]2dx

sin2(qLx/2)

(qLx/2)2

Disk (radius: R

infinitely thin)

Rod (length: L

infinitely thin)

By setting L = 0 2 - J1(2qR)/qR

q2R2

By setting R = 0 qL

0

qL2 sin(t)

tdt -

sin2(qL/2)

(qL/2)2

“Structure Analysis by Small Angle X-Ray and Neutron Scattering” L. A. Feigen and D. I. Svergun

Scattering Form Factors


Biological membranes deliver• Protection (separate cells)

• Signaling (transport of information)

• Selective permeability (transport of matter)

DPPC bilayer simulations by [email protected]

• Active functions are mainly providedby proteins

• Functionality depends strongly on thestructure of a lipid matrix

• Lipid matrix is a 2D liquid, where lipidsand proteins diffuse almost freely

Biomimetic Systems


• neutron scattering data are inherently featureless

• however, the mid-q region provides stronginformation on bilayer overall structure, reflecting the large scattering contrast between the lipid bilayer (a lot of H) and solvent (D2O)

0.01 0.110

-5

10-3

10-1

101

103

I(q)

[cm

-1]

q [Å-1]

bilayer overall

structure

bilayer inner

structure

Kučerka,N., J.F.Nagle, S.E.Feller and P.Balgavý, Phys.Rev.E (2004)

Neutron Scattering = Simple Models


• high resolution X-ray scattering data allows

for using complex models, thus enhancing the

spatial resolution of the bilayer structure

D'B

2DC

Total

MethylCG

P

CH2

Water +

Choline

-30 -20 -10 0 10 20 300.0

0.1

0.2

0.3

0.4

ele

ctr

on d

ensity

[e/Å

3]

z [Å]

N.Kučerka, S.Tristram-Nagle, J.F.Nagle, BJLetters (2006)

X-ray Scattering = Complex Models


Scattering Density Profile analysis• The same functional form for all of the

different contrast conditions (X-rays and neutron contrast variation)

• Volume distributions satisfy a spatial conservation principle

The SDP model is fit simultaneously to the different contrast conditions.

N.Kučerka, J.F.Nagle, J.N.Sachs, S.E.Feller, J.Pencer A.J.Jackson, and J.Katsaras, BJ (2008)

Joint Refinement = Advanced Models


Lipid Rafts by Neutron Scattering

Heberle, Petruzielo, Pan, Drazba, Kučerka, Standaert, Feigenson, KatsarasJACS 135 (2013)

Neutron scattering (via selective deuteration) is sensitive to nanometer-sized domains, previously not accessible by other methods.

The study of complex membrane models, including functional domains,helps to furtherour understandingof how the cell mayregulate criticalbiological processvia the compositionof lipid bilayers.







Beyond Scattering Experiments Beyond Scattering Experiments

detailed structural information

hydrogen bonding interactionslipid – cholesterol - water

SIMulation to EXPeriment analysis• MD simulations aid the analysis of experiment

• experimental results help to improve simulations

• direct comparison reconciles simulation and experiment

N. Kučerka, J. Katsaras, and J.F. Nagle, J. Mem. Biol. (2010)

MD Simulations = beyond advanced


MD Simulations + Experiment = beyond advanced

Structure-Function CorrelationJ.Karlovská, D.Uhríková, N.Kučerka, J.Teixeira, F.Devínsky,

I.Lacko and P.Balgavý, Biophys. Chem. 119 (2006)

N.Kučerka, J.Gallová, D.Uhríková, P.Balgavý, M.Bulacu, S-J.Marrink, and J.Katsaras, Biophys J (2009)


SAS is a valuable tool for structural biophysics allowing the in situ measurements of systems between 10 to 1000 Å

The scattering function is proportional to the product of form factor (intraparticle scattering function) and structure factor (interparticle interactions)

Overall morphology can be obtained through model independent approach, while model-based analysis provides further details on various structural parameters

Neutron scattering gives bases for simple models

High resolution X-ray scattering allows using advanced models

MD simulations provide further details on structure and interactions

MD + X-rays + neutrons provide a complete picture

Direct comparison of SIMulation to EXPeriment provides a tool for tweaking MD force fields and/or SDP models

norbert kučerka

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