Second Winterschool on Biomolecular Solid-State NMR

Stowe, Vermont  January  24-­‐29,  2010  

An Introduction

Shimon Vega Weizmann Institute of Science

with Yonatan Hovav & Akiva Feintuch

Dynamic Nuclear Polarization

MAS DNP static DNP + dissolution

for his successful development of high-field DNP for sensitivity enhancement in solid-state MAS NMR

Golman’s group (2003) GE HealthCare, Malmo

Dissolution DNP

Solid-State DNP-NMR

Bruker Biospin Corp.

The HyperSense

Oxford Instruments Ltd.

1960 – 1980 Abragam ; Goldman ; Hauser

1950 – 1956 Overhauser ; Slichter

1980 – 1995 Wind ; Yanoni ; Schaefer

Since the 50’s DNP has been there

all the time

many others

Sorry for not mentioning them

BDPA

4-amino TEMPO!

•!N ! O!H2N !

Trityl Bis TEMPO n-ethylene glycol!

glyserol/water DMSO/water Urea/water

consider a dilute [e-] system

TOTAPOL 1 electron 103-4 nuclei

electron : DNP : core nuclei : spin diffusion : bulk nuclei

The Hyperfine Interaction

EPR spectrum

B0

e- : n :

DNP: the solid effect

ωe + ωn

T1e T1,2x

T1n

T1n

T1e

T1e T1,2x

T1n

T1n

T1e

The populations Pn(t) during two Relaxation Mechanisms

and one Saturation MW

1

3 4

2

T1e relaxation

MW at saturation

T1n relaxation

pop

ulat

ions

T1e<<T1n,x

“saturation condition + T1e process”

Pe(t)

Pn(t)

SE-DNP conditions:

( sω1 )2 T2x <<T1n

with the right relaxation parameters and sufficient mw irradiation power one electron “could” polarize all its neighboring (core) nuclei

all other nuclei will be polarizes via Spin Diffusion

Spin Diffusion is energy conserving

and requires

energy level matching

hyperfine interactions is r-3 dependent

and results in

energy level mismatch

for the polarization of the core see elsewhere

The “core” of a simple cubic proton lattice

x

x

y

z z

y

“Spin diffusion”

there can of course be an A+ and a T1n distribution around e-

Pn

EPR: the electron g-tensor

β

α

the nuclear polarization as a function of the g-tensor orientation in the field

off resonance effects

only a small fraction of the electrons are active SE-DNP centers

Solid vs Cross Effect DNP

Griffin’s biradical BT2E at low concentration

40mM

10mM

SE vs CE

TM

The Cross Effect of two coupled electrons

e1 n

e2

D1,2/1nm~53MHz

1:

2

2

2

2

1 1

1 1

2

2

1

1

e1 n

e2 2:

The Cross Effect relies on mixing of non-directly

interacting degenerate states MW irradiation

1:

2

2

2

2

1 1

1

2

2

1

e1 n

e2 2:

The Cross Effect relies on mixing of non-directly

interacting degenerate states T1e relaxation

1

1

CE at both frequencies

1. It seems to be easier to saturate during CE than SE 2. The off resonance condition is like EPR

3: The enhancement of the core nuclei seems only a bit more complicated to describe; e.g. when A(1-n)=A(2-n)

CE CE SE

“(ω1MW)2T1eT2” ω1MW~Dee

e1 n

e2

Pn

MW

1,5

2,3,6,7

4,8

1,2

7,8

3,4,5,6

popu

lation

s

0 T1e e1

e2 For simplicity A(2-n)=0

popu

lati

on

Time (µs)

Populations

for the polarization of the core see elsewhere

θ

ϕ

Δβ=500

(θ,ϕ)

Cross effect condition

only a fraction of the electrons are active CE-DNP centers

95GHz DNP Spectrometry combining EPR & NMR

Daniella Goldfarb, Yaakov Lipkin, Yehoshua Gorodetsky, Akiva Feintuch

Home-made 95GHZ pulsed EPR microwave bridge: Bandwidth: 1GHz Max Output power: ~700mW Adjustable power and phase

Preliminary results (40K): Nutations:

/me  [µs]

/me  [µs]

DNP  freq.  sweep

Frequency  [GHz]

40mM  TEMPO  in  50:50  glycerol:H2O   1mM   Gd   in   50:50  Glycerol:H2O

40mM  trityl  in  50:50  Glycerol:D2O  

DNP frequency sweep 40mM TEMPO in 50:50 glycerol:H2O

Buildup - Decay down

MW NMR detection

prot

on s

igna

l Yonatan Hovav, Akiva Feintuch and Daphna Shimon:

e n

n `e e

`e `e

T1e T1D T1n MW

Cross Effect DNP vs high field Thermal Mixing DNP

ωe

ωe

ωe

ωe

ωe

“A model”

e

n

e1 ek

em en

This electron is coupled to its neighboring electrons, via dipolar diagonal and flip-flop terms

causing shifts and mixing

when they are close and in the right relative reorientation

when they are close in space but not oriented properly

re-e De-e biradical: 13 A ~25 MHz 40 mM 40 A ~0.8 MHz 10 mM 55 A ~0.3 MHz

Me

(M-1)e

A nucleus finds itself close to one of the electrons

e1

MW

e2

e

n

e1 e2

e4 e3

ene

rgy

e1

MW

e2

e

n

e1 e2

e4 e3

Populations

T1e

e1

MW

e2

e

n

e1 e2

e4 e3

That part of the Populations that is “active” due to the MW:

the nuclear signal MW+T1e

See you later for further explanations

Why do I think that I am cold without knowing my temperature?

M+1

M

M-1

“T” schematic energy – population

plot E

P P

The Bloch equation for a two level system

m(t) Ω

Appendices:

dispersion

absorption

http://www.uni-stuttgart.de/gkmr/lectures/lectures_WS_0203/magnetisation_blochequ.PDF

Saturation factor

cw-Steady state solutions

dynamics at the saturation

condition :

Degenerate perturbation theory

Approximate eigenfunctions