SPETTROSCOPIA DI NEUTRONI

Proprietà fondamentali del neutrone Relazione tra energia, impulso e lunghezza d’onda: ordini di grandezza… Elettricamente neutro Spin 1/2

SPETTROSCOPIA DI NEUTRONI

SPETTROSCOPIA DI NEUTRONI

Sezione d’urto doppio differenziale

Q : vettore d’onda scambiato tra neutroni e campione Q ~ Å-1 E : energia scambiata E ~ meV ≡ 8 cm-1 ≡ 0.24 THz

Fattore di struttura dinamico coerente (correlazioni tra posizioni di particelle diverse (jk), in funzione del tempo)

Fattore di struttura dinamico incoerente (correlazioni tra posizioni di una stessa particella (kk), in funzione del tempo)

),(),(2

EQSEQSdEd

dincinccohcoh σσσ

+∝Ω

( )[ ] ( )[ ]∫ ∑∞

∞−

− ⋅⋅−∝jk

kjti

coh tiiedtEQS RQRQ

exp0exp),( ω

( )[ ] ( )[ ]∫ ∑∞

∞−

− ⋅⋅−∝k

kkti

inc tiiedtEQS RQRQ

exp0exp),( ω

Fattore di struttura dinamico coerente (correlazioni tra posizioni di particelle diverse, in funzione del tempo) Elastico Fattore di struttura statico Struttura

Anelastico Fluttuazioni di densità, onde “sonore” (THz !) Curve di dispersione Velocità del “suono” Fattori di smorzamento Libero cammino medio

( ) [ ] ( ) ( )][1)(),( s2

ss1 qGQεQQ

G+−⋅−⋅+⋅∝ ∑∑+ δδ EEEnEScoh

( )∫= dEEQSQS cohcoh ,)(

0 5 10 15 20 250.0

0.5

1.0

1.5

2.0

D2O

S(Q)

Q (Å-1)

Fattore di struttura dinamico incoerente (correlazioni tra posizioni di una stessa particella, in funzione del tempo)

Quasielastico Dinamica “diffusiva” e coefficienti di diffusione D Ad esempio:

Anelastico Densità degli stati vibrazionali G(E) < u2 >

( ) ( )∫∝∝ max

0 22

2

2 1e),(E

inc EGE

dEuEGEQEQS

DE

EQSinc ∝ΓΓ+

Γ∝ con),( 22

Fully deuterated C-Phycocyanin in D2O.

«These modes are tentatively interpreted as due to short-lived coherent excitations propagating with velocities between 2000 and 4000 m/s... »

«A detailed quantitative interpretation of the data presented here is hardly possible because of the poor statistics…»

The first neutron Brillouin spectra of a biological sample…

Nowadays X-rays can provide a powerful tool…

… but do not allow contrast methods… …(and may induce radiation damages on biological samples?)…

Krisch et al., PRE 73, 061909 (2006)

Oriented Fibers of DNA

Liu et al., PRL 101, 135501 (2009)

Globular protein BSA

Sample Hydration Level

Hydrogenated RiboNuclease + D2O

(m ~ 6 g)

dry h = 0.0

wet h = 0.7

Hydrogenated DNA + D2O

(m ~ 6 g)

dry h = 0.0

wet h = 1.0

wet h = 15.0

Deuterated Escherichia coli

(m ~ 7.5 g)

Natural h ≈ 3

Samples & Measurements

The H/D contrast highlights the coherent signal of water against the incoherent signal of the biomolecule

BRISP spectrometer @ ILL - Ei = 83.7 meV, δE = 2.7 meV, T = 300 K

Data Treatment

Corrections for:

- background and cell scattering

- detector efficiency

- sample self-absorption

- multiple scattering

Water contribution: Iwater(Q,E) = Iwet(Q,E ) – Idry(Q,E )

[ ] [ ] [ ] [ ] [ ]

++

+++

+=

22222222 )(Γ)()(Γ)(

)(Γ)()(Γ)(1)(

)()(),(

EQQEEEQQa

EQQEEEQQaEn

EδQaEQS

LL

LL

HH

HH

QE

--

Model: elastic delta function + double DHO

0

10

20

30Q = 0.8 Å-1

RNase0.7h

0

10

20

S (Q,

E ) (

arb.

u.)

DNA15h

-20 -10 0 10 200

10

20

E (meV)

E. coli

Hydration Water Spectra

0

5

10

15

20Q = 0.4 Å-1

0

5

10

15 Q = 0.6 Å-1

S wate

r(Q,E)

(arb.

u.)

-20 -10 0 10 200

5

10

15 Q = 0.8 Å-1

E (meV)

RNase h = 0.7

DNA h = 15

E. coli h ≈ 3

Q = 0.8 Å-1

Q = 0.6 Å-1

Q = 0.4 Å-1

-20 -10 0 10 20

E (meV)

Q = 0.8 Å-1

Q = 0.6 Å-1

Q = 0.4 Å-1

-20 -10 0 10 20

E (meV)

Close similarity between hydration water and bulk water the biomolecule has small effect on the vibrational frequencies

Dispersion Curves

3400 m/sDNA 1.0h

E. coli ~3h

01020304050

3460 m/sE DH

O (m

eV)

0.0 0.4 0.8 1.2 1.6

hydration water bulk water

3500 m/sDNA15.0h

Q (Å-1)

RNase 1.0h

0.0 0.4 0.8 1.201020304050

3500 m/s

Larger damping than in bulk water a “glassy” dynamical behavior?

Intermediate damping in E. coli a “mixture” of waters h = 0.9

Damping Factors

Q 1.9

020406080 Q 1.5

Γ (

meV)

E. coli ~3h

DNA 1.0h

DNA15.0h

RNase 1.0h

0.0 0.4 0.8 1.2 1.6

Q 2.2

Q (Å-1)

0.0 0.4 0.8 1.2020406080

hydration water bulk water

Q 2.0

More about the “glassy” dynamics of hydration water…

A perdeuterated protein by the ILL Deuteration Lab: D-MBP

…hydrated with hydrogenated water…

…allows a reliable measurement of the hydration water incoherent dynamic structure factor

Measured on IN5 @ 100 K 0 4 8 12 16 20

0.0

0.2

0.4

0.6

0.8

1.0 MBP(D)-H2O MBP(H)-D2O MBP(H)-H2O

S (2θ

,E )

(arb

. u.)

E (meV)

Hydration Water Density of States…

The DoS of hydration water is

correctly reproduced only by a linear combination of the DoS of Low-Density and High-Density Amorphous Ice.

0.0

0.2

0.4

0 4 8 120.0

0.2

0.4

Hydr. Water Ih ice

G(E )

(m

ode/

meV)

Hydr. Water HDA ice LDA ice

E (meV)

…in the MBP protein

A general dynamical property of interacting water ?...

Interaction with a hydrophilic molecule… (globular protein, DNA helix, whole E. coli cell, nanoparticle…)

Distortion of locally ordered tetrahedra…

Role of the hydrogen bond network…

An alternative way to distort hydrogen bonds…

P = 200 MPa T = 268 K

Pure water under pressure

Diffusive dynamics vs. P and T

IN5

An alternative way to distort hydrogen bonds…

An alternative way to distort hydrogen bonds…

Further dynamical anomalies, again

at Q ~ 0.3 – 0.5 Å-1 …

…which diverge toward the elusive

second critical point (Widom line)…

Divergenza del tempo di residenza a Tc = 218 ± 5 K