SCATTERING OF NEUTRONS AND X-RAYS

ki

ki - kf = qhω ENERGY TRANSFER

hq MOMENTUM TRANSFERkf

Dynamic structure factor

O

r,t

COHERENT INCOHERENT

SCATTERING SCATTERING

g (r,t) gs(r,t)

QUASIELASTIC DIFFUSIVE MOTIONS

INELASTIC VIBRATIONAL

COHERENT INCOHERENT

STRUCTURAL FT [gs (r, )]

NUCLEAR PROB.

DISTRIBUTION

ELASTICElastic

QuasielasticInelastic

Energy transfer, ω

Δωe

Δωqe

S (q,ω) = ei(ωt-q·r) g(r,t) dr dt

Neutron Diffraction

1) Scattering from nuclei- combined x-n analysis of small molecules.

2) Scattering power does not depend on atomic number.- hydrogens scatter strongly- deuterium and hydrogen opposite signs.

3) Small-angle scattering - contrast matching.4) Solution scattering with isotope substitution

- partial structure factors.4) Enzyme structures

- proton positions- water structure

- no solution to phase problem- large crystals required- need nuclear reactor or spallation source.

Protein Hydration.

Svergun et al: First 3Å hydration layer ~10% denser than bulk water

FRANCI MERZEL

Geometric Rg from MD simulation = 14.10.1Å

SMALL-ANGLESCATTERING

RADII OF GYRATION

Statistical Models of a Strongly Unfolded Protein

Low q :Size

Radius of Gyration (Rg)

Include Higher q :Chain Configurational

Statistics

q(Å-1)

P(q)

Small Angle Neutron Scattering

rijbibj

0 0.1 0.2 0.30

0.2

0.4

0.6

0.8

1

ki

kf

ki

kfq

array detector

Sample

L ~ 5 - 50 m

n

1i

n

1jji qrij

qrsin ijbb

n21

)q(PqR

3

11~)q(P 2

g

0q

P(q)

q(Å-1)

Freely Jointed Chains Excluded Volume Chains

Phosphoglycerate Kinase in 4M GdnDCl

RgNat~ 23Å

RgDen~ 90Å

FJChains

0 0.1 0.2 0.31

2

3

0 0.1 0.2 0.31

2

3

x 10 A-4 -2o

q P(q)2

q(A )-1o

EVC6_1.0

Best FJC

EVC5_0.7

ANDREI PETRESCUPATRICK CALMETTESDOMINIQUE DURAND

EVB(Exluded Volume

Beta)

EVN(Exluded Volume

Native)

Ci-1

Ci

C,i+1

Low Resolution MC Simulation

Scattering Profile of the Models

Atomic Level Modeling

0 0.1 0.2 0.3 0.40

1

2

3

4

5

6

EVN

LE

EVB

x 10 A-4 -2o

q P(q)2

q(A )-1o

LE(Locally

Extended)

EVN

EVB

LE

EVN

EVB

LE

Snapshots of Atomic-Detail Models of Strongly-Unfolded PGK

Lattice Vibrations - PERIODIC in TIME and SPACE. - DISPERSION RELATIONSHIP between FREQUENCY and WAVEVECTOR

OPTICAL

ACOUSTICAL

0*a

q

1

l

=180o==2lq=/l

COHERENT INELASTIC NEUTRON SCATTERING

CRYSTALLINE L-ALANINE : LATTICE DYNAMICS

EXPERIMENT - Triple-Axis Coherent Inelastic Neutron Scattering

THEORY - (i) Ab Initio Quantum Chemistry

H-Bond and Rotational Potentials (ii) Energy Minimization + Harmonic Analysis.PHONON DISPERSION CURVES

CM-1THz

Calculated Experimental

COHERENT INELASTIC NEUTRON SCATTERING INTENSITIES22

.)( eQqF

INTENSITY SCATTERINGVECTOR

MODE POLARIZATION VECTOR

CALCULATED

EXPERIMENTAL

b*direction

UREA-ALKANE INCLUSION COMPOUND

DIFFUSIVE ALKANE DYNAMICS AT 180K

Three SimulationModels

Urea ‘HOST’

C19H40 ‘GUEST’

QUASIELASTIC INCOHERENT NEUTRON SCATTERING

Experiment compared with Simulation

DIRECTION PARALLELTO CHAIN AXIS

DIRECTION PERPENDICULARTO CHAIN AXIS

= experiment

1 chain

3 chains

5 chains

10 chains

ROTATIONAL PROBABILITY DISTRIBUTIONS OF ALKANE CHAINS

ROTATIONAL ANGLE,

TWO SINGLE CHAINS

Average Over Chains

V()=RotationalPotential

Potential of Mean Force=-kTlogP()

Elastic Incoherent Structure Factor

Experiment & Simulation

Converged (t)

2)(( PFT

Probability Distributions, P()