High Frequency Dynamic Nuclear Polarizationwinterschool.mit.edu/sites/default/files/documents/... · 2016-01-10 · Temperature and Field Dependence 1 10 100 300 0.01 0.1 100 Temperature

Biomolecular NMR Winter School Trap Family Lodge

January 10-15, 2016

High Frequency Dynamic Nuclear Polarization

Francis Bitter Magnet Laboratoryand

Department of ChemistryMassachusetts Institute of Technology

AMUPol

• Background and RationaleDNP, EPR, Signal to Noise and bRDNP Enhancements of 100-400 in MAS Spectra @ 90 KDNP functions quite effectively in multiple classes of systems

• CW DNP Mechanisms and Polarizing AgentsSolid Effect — δ ~Δ << ω0I

two spins, without e- - 1H hyperfine couplingOverhauser Effect — δ ~Δ << ω0I

two spins, with e- - 1H hyperfine coupling Cross Effect — δ < ω0I < Δ

three spins, with e- -e--1H dipole coupling

• Time Domain DNP — NOVELNOVEL — lab frame-rotating frame cross-polarization

• Instrumentation for DNPQuadruple Resonance, LT MAS ProbesSuperconducting Sweep CoilsGyrotron Microwave Oscillators and Amplifiers

NEW

NEW

DNP Outline








NEW

NEW

DNP Outline

What are the THREE most important parameters in magnetic resonance

Signal-to-noise

Signal-to-noise

Signal-to-noise4

Nuclear Spin PolarizationTemperature and Field Dependence

1 10 100 300

0.01

0.1

100

Temperature (K)

10

1

0.001

0.0186 % 1H polarization @ 700 MHz / 90 K

POLARIZATION

• Current strategy -- increase the polarization by increasing B0 ! • Result -- “modest” increases in sensitivity and resolution ! Increases in magnet cost are non-linear !

P = n+ - n-

n+ + n- = tanh γ !B0

2kT⎛⎝⎜

⎞⎠⎟

500 MHz

900 MHz

P = γ !B0

2kT

Electron and Nuclear PolarizationTemperature and Field Dependence

12.24 % e- polarization @ 700 MHz / 90 K

0.0186 % 1H polarization @ 700 MHz / 90 K

POLARIZATION

• Much larger spin polarization is present in the electron spin reservoir •Transfer the electron polarization to the nuclear spins by irradiating the electrons with high frequency microwaves !

P = n+ - n-

n+ + n- = tanh γ !B0

2kT⎛⎝⎜

⎞⎠⎟

(γe/γ1H) ~ 660 P = γ !B0

2kT

7Li w/ DNP @ 84 MHz

7Li w/o DNP

1H glycerol

• 7Li NMR @ ω0/2π= 50 kHz (30.3 Gauss)

• EPR @ ω0/2π= 84 MHz

ε ~ 100

• Initial demonstration of the Overhauser effect -- DNP • Nuclear Overhauser effect is important in solution NMR !

Carver and Slichter, Phys. Rev. 92, 212-213 (1953) Phys. Rev. 102, 975-980 (1956)

1950’s -- Overhauser Experiments in Metals (0.00303 T, 84 MHz) -- A. Overhauser, Phys Rev (1953); T. Carver and C.P. Slichter, Phys Rev (1953, 1956) 7Li , 23Na, 1H in NH3

1960-1980 -- Liquids and Solids (0.3300 T, ~10 GHz) Liquids -- Hauser, Mueller-Warmuth, Richards, and others Solids -- Abragam, Goldman, Atsarkin, Provotorov, and others Nuclear magnetic ordering, polarized targets for particle physics, liquids at low fields

1990 -- Current (5-17 T, 140-460 GHz) Gyrotron based high field experiments@ MIT Amyloid and membrane peptides and proteins, biological samples, liquids

DNP - brief history

Overhauser Slichter

Abragam Goldman

Melissa Hornstein and her 460 GHz gyrotron oscillator

1980’s -- MAS Experiments on Solids (1.5 T, 40 GHz) R.A. Wind, C.S. Yannoni, J. Schaefer Polymers, carbonaceous materials, diamond, etc.

Yannoni Wind Schaefer

Sample Preparation

• TOTAPOL is soluble in water and stable

• Cryoprotection is critical to minimize inhomogeneous broadening

• Polarization diffuses throughout the macromolecule

H2O e

-

H2OH

2O

e-

e-

e-

e-

e- H2O

H2O

H2O

H2O

H2O

H2O

e-

Purple membrane

Cryoprotected sample

Cryoprotectant (e.g. glycerol)

bacteriorhodopsin

1. Resuspension

2. centrifugation

TOTAPOL Sedimented Proteins

“DNP Juice”

d8-glycerol/D2O/H2O

60:30:10

Quadruple Resonance DNP/MAS Probew/ Optical Irradiation of the Sample

• Quadruple resonance -- 1H, 13C, 15N, and e-

• Routine low temperature spinning at 85-90 K, ωr/2π ~10 kHz• Optical irradiation (532/650 nm) of samples to generate photochemical

intermediates

Barnes, et. al. JMR (2009)

MAS and Sample Exchange

3D printed eject pipe

tapped waveguide

Barnes et al. JMR, 198(2), 261

custom 3.2 mm Lewis stator

• Changes samples in minutes • Reduces risk of damage

90° turn

80-100 K

Simulation of EM Coupling to Sample

l The full system was modeled in HFSS l Internal Reflections

Top View

Side View

Sapphire Rotor

EM Waves Launched

NMR Coil

• Modeling useful to optimize coupling of EM radiation to sample

8 mm

E. Nanni and R. Temkin, 2010

DNP in Nonconducting Solids

♦ Requires microwaves and cryogenic temperatures

2H

2H

2H2H 2H

2H

2H

2H

2H

2H

2H2H

2H

2H

2H

2H

2H2H

2H

2H

DNP Sensitvity Enhancement

♦ ε = 40: DNP – 1 Day; no DNP – 4.38 years

AMUPol Biradical Paul Tordo and Co.

Aux Marseille Universite

♦ ε = 420: DNP – 1 Day; no DNP – 483 years !

ε = 420

Qing Zhe Ni1M-13C-urea / 10 mM radical 60/30/10 (v/v/v)

380 MHz / 250 GHz - mw ~ 12 W

T=78 K, 13C{1H} CPMAS, 5.5 kHz

35 MHz e--e-

coupling

Bacteriorhodopsin

Cytoplasm

Extracellular medium

D96

K216

D85

D212

Luecke et al, J. Mol. Biol. 291, 1999, 899.

•26 kDa membrane protein

•Retinylidene chromophore

•Light-driven proton pump

•Pump mechanism unknown

•Mechanism of H+ pumping ?

• Polarize the 15N Schiff base in the center of the bilayer !

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

• Electrons in the solvent !

ε=+52 250.572 GHz10 W10 kV, 190 mA

MW off (x10)

all spectra:U-[13C,15N,1H]-bR81 Kelvin4 kHz MAS50 mM TOTAPOLB0 = 8.934 Tesla B0 = 380.378 MHz 1HGyrotron = 9.12 Tesla

0

ε=-42251.112 GHz9W8.8kV, 190 mA

5010015020025013C (ppm)

DNP Enhancements on Membrane Proteins

bacteriorhodopsin (bR)

• Tunable gyrotron has 3 GHz bandwidth -- covers the + and - enhancements with nitroxide radicals

(+72)

Daviso, Ni, Barnes (2012)

e-e-

e-e-

e-e-

e-e-

e-e-

e-

e-

e-

e-e-e-

e-e-

e-

e- e-e-

DNP in Membrane ProteinsDistribution of Polarization via 1H Spin Diffusion

• Polarize the solvent 1H with biradicals and CW μwaves• 1H spin diffusion distributes the polarization to the protein

=biradical polarizing agente-e-

e-

e-

=cryoprotectant

~50 Å

DNP Enhanced 15N MAS Spectra of U-13C,15N-bR Are we polarizing the entire protein ? YES !

Bajaj, Mak, Belenky, Herzfeld, Griffin (2009)

ArgLys

Integrals of the resolved lines (10-20% error)

Three previous publications ....

Rosay, et al JACS 123, 1010-1011 (2001) Rosay, et al JACS 125, 13626-27 (2003) van der Wel JACS 128, 10840-10846 (2006)

e-e-

e-e-

e-e-

e-e-

e-e-

e-

e-

e-

e-e-e-

e-e-

e-

e- e-e-

DNP in Membrane ProteinsDistribution of Polarization via 1H Spin Diffusion

• Polarize the solvent 1H with biradicals and CW μwaves• 1H spin diffusion distributes the polarization to the protein

=biradical polarizing agente-e-

e-

e-

=cryoprotectant

~50 Å

Intermolecular constraints mixed [15N]/[13C] labeling

• Fibrils formed from a 1:1 mixture of 15N monomers and 13C monomers (using [2-13C]glycerol)

• Protein molecules are incorporated randomly into the fibril

fibril axis

Crh dimer: Etzkorn, Baldus, Boeckmann et al. JACS 2004 Thioredoxin: Yang, Polenova, et al. JACS 2008 HET-s prion: Meier, et al. Science 2008, JACS 2010 GB1 crystals: Nieuwkoop and Rienstra. JACS 2010 β2-microglobulin fibrils: Debelouchina, Griffin, et al. JACS 2010

Intra-‐sheet constraints with DNP: PI3-‐SH3

b2m

MHC-‐I 300 K 750 MHz 16 days

100 K with DNP 400 MHz 1.5 days

Many more intermolecular constraints are obtained with low-‐temperature DNP spectra.

Bayro MJ, Debelouchina GT et al., JACS, 2011, 13967

23 constraints

52 constraints

• 15N-13Ca and 15N-13Cb cross-peaks between adjacent β-strands

• Define parallel, in-register structure

• Other constraints: to be determined/assigned

Intermolecular 15N-13C constraints Aliphatic region

750 MHz

400 MHz

Adam’s Needles MxiH Protein in T3SS Needles

Fricke, et al ChemPhysChem 2014, 15, 57 – 60

• 600 MHz/395 GHz • 13C-13C -PDSD, ℇ=20 • Resolution of ~1 ppm • 3D NCC spectra

Anne, Guido and Lyndon’s Virus Particle 400 and 800 MHz

Lesage, Pintacuda and Emsley (2014)

• Resolution increases at higher fields !

DNP Worldwide

400 MHz/263 GHz H. Oschkinat/Berlin

G. Bodenhausen/Lausanne

M. Baldus/Utrecht

G. DePaepe/Grenoble

C. Glaubitz/Frankfurt

M. Rosay/Billerica

600 MHz/395 GHz A. McDermott/ Columbia

V. Ladizhansky/Guelph

C. Greisinger/Lausanne

J. Long/ Florida State

H. Heise/ Dusseldorf

800 MHz/527 GHz M. Baldus/Utrecht

L. Emsley/Lyon

G. Bodenhausen/Paris

WS 2010 -- One student remarked that he/she “will not try DNP very soon” since ... there will not be access to DNP hardware in the near future !

Other efforts: R. Tycko, Songi Han, K. Zilm, M. Ernst, M. Levitt, C. Hilty, W. Koeckenberger, Dan Vigernon, etc.

>30

gyrotrons

Sensitivity Enhancement in MAS NMR

Method Δ CostEnhancement

εBoltzmann

Temperature Factor

Total

εTime

Savings400 MHz→>1000 MHz $ 16M 4 1 4 16

MAS cryoprobe $0.25 M 4 1 4 16

800 MHzDNP $1.5 M 60 3 180 32,400

Newradical ??? 85 3 255 65,000

Very substantial time savings available with DNP !

Sensitivity Enhancement in MAS NMR

Method CostEnhancement

εBoltzmann

Temperature Factor

Total

εTime

Savings400 MHz→1000 MHz $ 16M 4 1 4 16

MAS cryoprobe $0.25 M 4 1 4 16

800 MHzDNP $1.5 M 60 3 180 32,400

Newradical ??? 85 3 255 65,000

DNP is a synchrotron upgrade for NMR !








NEW

NEW

DNP Outline

DNP Polarizing AgentsMonoradicals -- Solid and Overhauser Effect

Biradicals -- Cross Effect

AMUPol

EPR spectra and DNP Zeeman field profiles

• EPR spectra of polarizing

agents -- ~100 mT (1000 G)

• Variety of polarizing agents

allows for optimal DNP in

different situations

140 GHz EPR spectra

DNP Zeeman field profiles

Mn2+

Gd3+

NO• BDPAtrityl

CW Dynamic Nuclear Polarization Mechanisms

Solid Effect (SE) -- single electron,insulating solids (organic, biological systems) when .…

δ ~Δ << ωδ = homogeneous linewidth of the EPR spectrum

Δ = breadth of the EPR spectrum ω = nuclear Larmor frequency (1H, 13C, 15N)

Overhauser Effect (OE) -- applicable to systems with mobile electrons -- i.e., metals, liquids, 1D conductors (Carver and Slichter, Li metal) and strong 1H hyperfine couplings

δ ~Δ << ω


Thermal Mixing (TM) -- multiple electrons, insulating solids, but ….

δ, Δ >> ω TM -- dominates when the g anisotropy is small, and/or the EPR line is

homogeneously broadened, and ω is small

Cross Effect (CE) -- two electrons, insulating solids, but ….

Δ> ω>δ CE -- operative at high fields where Δg >> δ, the line is inhomogeneously broadened.

Time Domain DNP Mechanisms

Pulsed DNP Weis and Griffin, SSNMR 29 105-117 (2006); Can, et al. J. Chem. Physics 2015. Mathies, et al. J. Phys Chem Letters (in press) 2016

Integrated Solid Effect -- Wenckebach (CPL, 1988) π -- CW on the electrons

NOVEL -- Wenckebach (CPL, 1988) rotating frame / lab frame

ω1e=ω0 RF DNP -- Wind and Co. (AMR, 1985)

High frequency microwave amplifiers are just becoming available.


Solid Effect (SE) -- single electron,insulating solids (organic, biological systems) when .…

δ ~Δ << ωδ = homogeneous linewidth of the EPR spectrum

Δ = breadth of the EPR spectrum ω = nuclear Larmor frequency (1H, 13C, 15N)

Overhauser Effect (OE) -- applicable to systems with mobile electrons -- i.e., metals, liquids, 1D conductors (Carver and Slichter, Li metal) and strong 1H hyperfine couplings

δ ~Δ << ω

Paramagnetic Centers for DNP

BDPA

Galvinoxyl

TEMPO

49.949.849.749.649.5

Field (kilogauss)

• EPR lineshapes are Dominated by g- anisotropy

• BDPA linewidth ~21 MHz ---- Solid effect

• TEMPO powder pattern~600 MHz ---- Thermal mixing or

cross effect

ωe/2π = 28 GHz/T

DNP with Gyrotrons

e- →1H→13C e- → 13Cεmax @ ωe ± ωn

ε~10 ε~40

1.5% efficient

(γe/γn) ~ 660

Trityl Radical Structure and FT EPR Spectrum

• Small g-anisotropy yields a solid effect enhancement mechanism

DNP Polarizing AgentsMonoradicals -- Solid and Overhauser Effect -- Δ=25-60 MHz

9 GHz EPR spectra16 1H couplings 21 1H couplings

Can, et al, J. Chem. Phys. 141, 064202 (2014)

Dynamic Nuclear PolarizationSolid State EffectDNPDNPDNP

• Enhancement ~ (γ ε / γ n ) (ω1 /ω0 )2 (Ne / δ )T1n

• Irradiate the flip-floptransitionsW±

NuclearZeeman

Bath

ElectronZeeman

Bath

EquilibriumNegative

EnhancementPositive

EnhancementNo

Enhancement

νε−νn νε+νnνε

|--) + q |-+)

|+-) - q |++)|++)+ q* |+-)

WEPR

WEPRW±

|-+) - q* |--)Wnmr

Wnmr

Solid Effect @ 400 MHz/263 GHz

• Mediated by single electron-nuclear spin flips

•Transitions are partially allowed due to state mixing.

•Maximum and minimum enhancements at ω =ωe ± ωn

Trityl Radical triphenyl methyl radical

Magne&c Field

Polarize ωe±ωn

C. Can, M.Caporini, F. Mentink-Vigier , S. Vega and M. Rosay, JCP (2014)

Dynamic Nuclear PolarizationSolid State EffectDNPDNPDNP

• Enhancement ~ (γ ε / γ n ) (ω1 /ω0 )2 (Ne / δ )T1n

• Irradiate the flip-floptransitionsW±

NuclearZeeman

Bath

ElectronZeeman

Bath

EquilibriumNegative

EnhancementPositive

EnhancementNo

Enhancement

νε−νn νε+νnνε

|--) + q |-+)

|+-) - q |++)|++)+ q* |+-)

WEPR

WEPRW±

|-+) - q* |--)Wnmr

Wnmr

State Mixing+ + S+ − − = + − S+ − + = 0 !

• Electron-nuclear transitions are forbidden

Perturbation Theory Notes 1

ψ n1 =

ψ m0 ′H ψ n

0

En0 − Em

0m≠n∑ Ψm

0 !

En1 = ψ n

0 ′H ψ n0 !

En2 =

ψ m0 ′H ψ n

0 ψ n0 ′H ψ m

0

En0 − Em

0 =m≠n∑ ′Hmn ′Hnm

En0 − Em

0m≠n∑ !

•Hamiltonian of interest is the electron-nuclear dipolar coupling

Electron-Nuclear Dipole Coupling

• C and D (C’) terms mix adjacent states

H IS =

γ Iγ Sr3

(A + B + C + D + E + F) !

A=(1− 3cos2θ) SZ IZ[ ]B = −

1

4(1− 3cos2θ) S−I+ + S+I−[ ]

C = −3

2sinθ cosθe− iφ S+IZ + SZ I+[ ]

D = C† = −3

2sinθ cosθeiφ S−IZ + SZ I−[ ]

E = −3

4sin2θe−2iφ S+I+[ ]

F = −3

4sin2θe2iφ S−I−[ ]


• Only terms with the nuclear frequency survive in the expansion

ψ 31 =

ψ m0 ′H ψ n

0

En0 − Em

0m≠3∑ ψ m

0 =ψ 1

0 ′H ψ 30

E30 − E1

0ψ 1

0 +ψ 2

0 ′H ψ 30

E30 − E2

0ψ 2

0 +ψ 4

0 ′H ψ 30

E40 − E1

0ψ 4

0

E30 − E1

0 =1

2γ SB0 +

1

2γ IB0

⎛⎝⎜

⎞⎠⎟−

1

2γ SB0 −

1

2γ IB0

⎛⎝⎜

⎞⎠⎟= γ IB0 = ω0 I

E30 − E2

0 =1

2γ SB0 +

1

2γ IB0

⎛⎝⎜

⎞⎠⎟− −

1

2γ SB0 −

1

2γ IB0

⎛⎝⎜

⎞⎠⎟= γ SB0 = ω0S

E40 − E1

0 = −1

2γ SB0 +

1

2γ IB0

⎛⎝⎜

⎞⎠⎟−

1

2γ SB0 −

1

2γ IB0

⎛⎝⎜

⎞⎠⎟= −γ SB0 + γ IB0 ≈ −ω0S

!

ω 0S / 2π = 140 GHz ω 0 I / 2π = 211 MHz


• Only terms with the nuclear frequency survive

ψ 31 =

ψ m0 ′H ψ n

0

En0 − Em

0m≠3∑ ψ m

0 =ψ 1

0 ′H ψ 30

E30 − E1

0ψ 1

0 +ψ 2

0 ′H ψ 30

E30 − E2

0ψ 2

0 +ψ 4

0 ′H ψ 30

E40 − E1

0ψ 4

0

E30 − E1

0 =1

2γ SB0 +

1

2γ IB0

⎛⎝⎜

⎞⎠⎟−

1

2γ SB0 −

1

2γ IB0

⎛⎝⎜

⎞⎠⎟= γ IB0 = ω0 I

E30 − E2

0 =1

2γ SB0 +

1

2γ IB0

⎛⎝⎜

⎞⎠⎟− −

1

2γ SB0 −

1

2γ IB0

⎛⎝⎜

⎞⎠⎟= γ SB0 = ω0S

E40 − E1

0 = −1

2γ SB0 +

1

2γ IB0

⎛⎝⎜

⎞⎠⎟−

1

2γ SB0 −

1

2γ IB0

⎛⎝⎜

⎞⎠⎟= −γ SB0 + γ IB0 ≈ −ω0S

!

ω 0S / 2π = 140 GHz ω 0 I / 2π = 211 MHz



ψ 31 =

ψ m0 ′H ψ n

0

En0 − Em

0m≠3∑ ψ m

0 =ψ 1

0 ′H ψ 30

E30 − E1

0ψ 1

0 +ψ 2

0 ′H ψ 30

E30 − E2

0ψ 2

0 +ψ 4

0 ′H ψ 30

E40 − E1

0ψ 4

0

q = −γ Iγ S

r3

3

2ω0 I

sinθ cosθe− iφ + + SZ I+ + −

ψ 3= + − − q + +



q = −γ Iγ S

r3

3

2ω0 I

sinθ cosθe− iφ + + SZ I+ + −

ψ 3= + − − q + +

ψ 1= + + + q * + −ψ 2 = − + − q * − −ψ 4 = − − + q − +

!

Transition Probabilities

ψ 1 S+ ψ 4

2= + +( ) + q + −( ) S+ − −( ) + q − +( ) 2

= 2q = 4q2 !

ψ 2 S− ψ 3

2= − +( ) − q − −( ) S− + −( ) + q + +( ) 2

= 2q = 4q2 !

Double Quantum

Zero Quantum

q2 ω0 I

−2 !

• Solid effect scales as ω 0−2 !

Solid Effect with Trityl Radical

• Soluble in aqueous media

• Frequency dependence shows a well resolved solid effect

• Peaks in the enhancement curves at ω e±ω n

δe < ω n90 MHz < 211 MHz

• Enhancements are significant but modest only ±15 ! L !K. Hu et. al (2004)

Solid Effect DNP

• Sta&c Hamiltonian: Hu et. al., JCP (2011) Corzilius JCP (2012)

• H can be diagonalized in 2 subspaces

Cody Can (2012)








NEW

NEW

DNP Outline

Lessons from Solu9on NMR๏ Overhauser effects require mobile electrons or nuclei....

Metals, 1D conductors, Na in NH3, solu&on NOE’s

๏ Heteronuclear Overhauser effects scale ~B0-‐n .... Transla&onal and rota&onal spectral densi&es Heteronuclear (1H-‐13C) NOE’s are aKenuated >2.3 T

Should not do 13C protein NMR above >60-‐100 MHz

๏ Time Domain Experiments are not field dependent .... INEPT for 1H-‐13C /15N polariza&on transfers

Overhauser DNP in insulators — new mechanism !

Overhauser DNP scales as B0 +n!

Pulsed DNP experiments are not field dependent !

Overhauser Effect vs. ω0

• Overhauser effects commonly scale ~ω0-n

•13C NMR in proteins — only at <100 MHz

Hauser and Stehlik Adv in Mag. Res 1970

Oldfield, Norton and Allerhand J. Biol. Chem. 1975

electron-nuclear 1H-13C NOE’s in proteins

7Li w/ DNP @ 84 MHz

7Li w/o DNP

1H glycerol

• 7Li NMR @ ω0/2π= 50 kHz (30.3 Gauss)

• EPR @ ω0/2π= 84 MHz

ε ~ 100

• Initial demonstration of the Overhauser effect -- DNP • Nuclear Overhauser effect is important in solution NMR !

Carver and Slichter, Phys. Rev. 92, 212-213 (1953) Phys. Rev. 102, 975-980 (1956)

Water soluble BDPA

• Improved Solid Effect

performance with MAS 40 mM in d8-Glycerol/D2O/H2O (60:30:10) 4 mm rotor spinning at 5 kHz, 80 K 5 W cw microwave irradiation

Olesya Haze, Tim Swager, et al. JACS (2012)

Solid and Overhauser Effects @ 400 MHz/263 GHz

•Small Overhauser enhancement for SA-BDPA

•Well developed transition for BDPA

•Trityl cannot make up its mind !

Solid EffectSolid Effect

+ Overhauser


Solid + Overhauser Effect @ 600 MHz/395 GHz

• Overhauser enhancement for

BDPA and SA-BDPA

• SA-BDPA -- 40 % of the SE

enhancement

• g-anisotropy evident on the SE

lineshape

• 800 and 1200 MHz ?

Abragam, A. Phys. Rev. 1955, 98, 1729–1735.Can, et al, J. Chem. Phys. 141, 064202 (2014)

DNP Polarizing AgentsMonoradicals -- Solid and Overhauser Effect -- Δ=25-60 MHz

9 GHz EPR spectra16 1H couplings 21 1H couplings


Solid + Overhauser Effect HYperfine Coupling Zero Quantum

• Overhauser and solid effect enhancements

• Two spin model -- 5 MHz 1H-e- couplings

• Zero quantum relaxation mediates the OE enhancement


Solid + Overhauser Effect


• Two spin model, 1H hyperfine coupling

• Zero quantum relaxation mediates the OE enhancementCan, et al, J. Chem. Phys. 141, 064202 (2014)

Solid + Overhauser Effect HYperfine Coupling Zero Quantum

63


• Two spin model -- 5 MHz 1H-e- couplings

• Zero quantum relaxation mediates the OE enhancement


Solid + Overhauser Effect Simulations

F. Mentink-Vigier and S. Vega

• Overhauser enhancement for BDPA and SA-BDPA

• Two spin model, 1H hyperfine coupling

• BDPA’s have 1H’s ! Trityl e--1H coupling weak !


Overhauser Effect Power Dependence F. Mentink-Vigier and S. Vega

• Zero quantum relaxation OE enhancement

• High frequency sources (400-1000 GHz), <5 watts


Solid + Overhauser Effect Dipolar Coupling Double Quantum


• e- -1H dipolar coupling

• Double quantum relaxation mediates the OE enhancementCan, et al, J. Chem. Phys. 141, 064202 (2014)

Solid + Overhauser Effect


• Two spin model, 1H hyperfine or dipolar coupling

• Zero or double quantum relaxation OE enhancement

e- -1H dipolar --DQe- -1H Hyperfine -- ZQ


Overhauser Effect vs. ω0

• Overhauser effects commonly scale ω0-n

• Solid effect scales ℇ0 ~ω0-2

• Overhauser effect scales ~(ℇ0 +k’ω0) [rather than ω0-n]

Marc Baldus Utrecht Univ.


Thermal Mixing (TM) -- multiple electrons, insulating solids, but ….

δ, Δ >> ω TM -- dominates when the g anisotropy is small, and/or the EPR line is



Δ> ω >δ CE -- operative at high fields where Δg >> δ, the line is inhomogeneously broadened.

Paramagnetic Centers for DNP

BDPA

Galvinoxyl

TEMPO

49.949.849.749.649.5

Field (kilogauss)

• EPR lineshapes are Dominated by g- anisotropy

• BDPA linewidth ~21 MHz ---- Solid effect

• TEMPO powder pattern~600 MHz ---- Thermal mixing or

cross effect








NEW

NEW

DNP Outline


Thermal Mixing (TM) -- many electrons, insulating solids, but ….

δ, Δ >> ω0 TM -- dominates when the g anisotropy is small, and/or the EPR line is



Δ > ω0 > δ CE -- operative at high fields where Δg >> δ, the line is inhomogeneously broadened.

DNP

0 200-200-400Frequency (MHz)

e1 e

2

ωn

Δ 600 MHz

δ ~5 MHz

ω0I

• Mechanism determined by relative size of Δ, ω0I ,δ

•Cross effect -- three spins Δ> ω0I/2π> δ

•Solid effect -- two spins ω0I/2π > δ,Δ

•Overhauser effect - mobile electrons

•Thermal mixing - many electrons, homogeneous EPR

• Time domain DNP — electron spin locking

DNP Mechanisms

DNP Polarizing AgentsMonoradicals -- Solid and Overhauser Effect

Biradicals -- Cross Effect

AMUPol

Cross Effect DNP Inhomogeneous EPR DNPDDNP

ε TM ∝B1

2

B0

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ T1e T1n

1. µwave irradiation and e--e- cross-relaxation burn a hole in the EPR line.

EPR Intensity


e1 e

2

ωn

2. Two electrons separated by ω n flip-flop and the difference in energy is used to flip a nucleus.

τeen( )−1= 4 q

2 1

T2eS S

g(ω )g(ω −ωn )−∞

∞

∫g(0)

TEMPO EPRAbsorption Lineshape


µ-waves

ε ∼γ eγ N

657 for 1H

2615 for 13C

4. Enhancement

ω2e− ω1e= ωn3.

Monomeric Polarizing Agents

Purple membrane

Cryoprotectant (e.g. glycerol)

4-amino TEMPO

bacteriorhodopsin

1. Resuspension

2. centrifugation

• Randomly oriented and dispersed paramagnetic centers

• Suboptimal utilization of e--e- dipolar coupling

•N OH2N

weak e--e-

couplingstrong e--e-

coupling

Biradical Polarizing AgentsDNPDNPDNP

Bis TEMPO n-ethylene glycol(BTnE)

• Biradical consists of two stable radicals (TEMPO) tethered together by a linker (ethylene glycol).

• Used extensively in the 70’s for the study of dynamics with EPR.

• Currently employed in pulsed EPR investigations of distances in a variety of systems.

Kan HuBruce Yu

DNPDNPDNP Thermal Mixing/Cross Effect DNP

• NO! EPR spectrum is ~600 MHz wide

• Thermal mixing and the cross effect are …

three spin process

involving the irradiation of a dipolar coupled electron spin system

• Flip two electrons and then a nuclear spin.

C.F. Hwang and D.A. Hill, PRL18, 110-112 (1967)

DNPDNPDNP

3NO

•

N O•

N O•B 0

• Correct relative orientations of the TEMPO molecules are required to yield two lines separated by

ω2e- ω1e =ωnefficient thermal mixing/cross effect polarization transfer

• Simulations suggest that the TEMPO molecules in BTnE’s are oriented at approximately 90º with respect to one another

• g-tensor orientations yield two lines separated by ~ ωn/2π ?

Qualitative Thermal Mixing/Cross Effect DNP

g-tensor Orientations

DNPDNPDNP

NO

•

N O•

N O•

3B 0

Semi-quantitative Thermal Mixing/Cross Effect DNP

g-tensor Orientationse2

e1

• Several different orientations satisfythe frequency difference

ω2e- ω1e =ωn

AMUPol Biradical Paul Tordo and Co.

Aux Marseille Universite

♦ ε = 420: DNP – 1 Day; no DNP – 483 years !

ε = 420

Qing Zhe Ni1M-13C-urea / 10 mM radical 60/30/10 (v/v/v)

380 MHz / 250 GHz - mw ~ 12 W

T=78 K, 13C{1H} CPMAS, 5.5 kHz

35 MHz e--e-

coupling

Three-Spin Process in

Cross Effect DNPDNPDNPDNP

Ifωe2-ωe1~ωn

l-+->, l+-+>degenerate

ω e1 ω e2

DNP(-)MW

DNP(+)

EquilibriumΔωe < ωn

EquilibriumΔωe > ωn

SSI SSI

l++->

l-+->

l+-->

l--->

l+++>

l-++>

l+-+>

l--+>

EquilibriumΔωe = ωn

PositiveEnhancement

NMR

ω e1

NegativeEnhancement

NMR

ω e2

Kan Hu PhD Thesis

2006

Three Spin Cross Effect DNP• Hamiltonian:

= +

• Matrix form in direct product basis:

Unperturbed Perturba:onTotal

Cody Can (2012)• Thurber and Tycko, JCP (2012)

E3 =12

ω0I −Dd

2

⎛

⎝⎜⎞

⎠⎟− ωΔ +

AΔ

2

⎛⎝⎜

⎞⎠⎟

2

+D02

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

E6 =12

−ω0I −Dd

2

⎛

⎝⎜⎞

⎠⎟− ωΔ −

AΔ

2

⎛⎝⎜

⎞⎠⎟

2

+D02

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

ω0I ≈ ωΔ2 +D0

2

• !Diagonalizing!the!unperturbed!H0!

• !1st!matching!condi8on:!!1:1!state!mixing!due!to!the!degenerate!perturba8on!

• !2nd!matching!condi8on:!where!to!set!the!microwave!frequency!

Cross Effect Matching Conditions








NEW

NEW

DNP Outline

Overhauser Effects in NMR๏ Overhauser effects require mobil electrons or nuclei....

Metals, 1D conductors, Na in NH3, solu:on NOE’s

๏ Heteronuclear Overhauser effects scale ~B0-‐n .... Transla:onal and rota:onal spectral densi:es Heteronuclear (1H-‐13C) NOE’s are aPenuated >2.3 T

Should not do 13C protein NMR above >60-‐100 MHz

๏ Time Domain Experiments are not field dependent .... INEPT for 1H-‐13C /15N polariza:on transfers

Overhauser DNP in insulators — new mechanism !

Overhauser DNP scales as B0 +n!

Pulsed DNP experiments are not field dependent !

Time Domain DNP NOVEL - ω0I =ω1S

• NOVEL matching condition -- ω0I =ω1S

• n=4096 • 𝜏90X= 15 ns, 𝜏match=100 ns, 𝜏1=20 μs

•Lab frame/rotating frame matching -- Z-polarization

• Should not manifest a B0 dependence !

•Use pulses on the e- to build up polarization

Can, et al, J. Chem Phys 143, 054201 (2015)Henstra and Wenckebach, Mol. Physics (2008)

1H-13C/15N Cross Polarization Hartmann-Hahn - ω1I =ω1S

• # 1H spins ≥ # 13C spins • Generates transverse magnetization

B0 B0

B0 B0

ω1I

ω1S


• # e- spins < # 1H spins • Substitute the B0 field for B1S • Generates Z-polarization !

B0 B0

B0 B0

ω1S

ω0H

Henstra and Wenckebach, Mol. Physics (2008)

Spin lock the electrons

Davies ENDOR Spectrum Benzophenone-Diphenylnitroxide

•Crystal structure and molecular structure

•140 GHz Davies ENDOR spectrum

Can, et al, J. Chem Phys 143, 054201 (2015)


•Saturate 1H signals with a train of “m” pulses •Spin lock the electrons “n” times using ω0I =ω1S ! •Detect the signal with a solid echo


Microwave Field Profiles NOVEL - ω0I =ω1S


• Lab frame/rotating frame matching -- Z-polarization

• Should not manifest a B0 dependence !Henstra and Wenckebach, Mol. Physics (2008)

T=300 K

ℇ~300


NOVEL - ω0I =ω1S

Diphenyl-NO in Benzophenone



• Should not manifest a B0 dependence !Henstra and Wenckebach, Mol. Physics (2008)

300 ns


NOVEL at 80 K

• A factor of ~3 improvement by deuteration

• Also works well at low temperature

(b) SA-BDPA in DNP juice


NOVEL - ω0I =ω1S

Trityl DNP Juice



• Should not manifest a B0 dependence !Henstra and Wenckebach, Mol. Physics (2008) Mathies, et al JPC Lett (2016)

NOVEL - ω0I =ω1S

Trityl DNP Juice



• Should not manifest a B0 dependence !Henstra and Wenckebach, Mol. Physics (2008) Jennifer Mathies (2014)

1 µs

NOVEL - ω0I =ω1S Trityl DNP Juice



• Should not manifest a B0 dependence !Henstra and Wenckebach, Mol. Physics (2008) Jennifer Mathies (2014)

15 MHzℇ~400








NEW

NEW

DNP Outline

140 GHz Pulsed DNP Spectrometer Gyro-Amplifier

• Gyroamplifier currently generating ~800 watts • Quasioptical bridge for detection • Time domain DNP -- no field dependence • Experimental flexibility

Andy Smith and Bjoern Corzilius

Time Domain DNP Spectrometer (of the future)

•Gyroamplifier, corrugated waveguide, NMR and EPR consoles

•Quasi-optic network -- λ ~ 2.14 mm (140 GHz) to 0.57 mm (527 GHz)

• Ernst and coworkers -- time domain NMR !

140 GHz Pulsed DNP Spectrometer MAS Probe

• Gyroamplifier generating ~400-1000 watts • Quasioptical bridge for detection • Time domain DNP -- no field dependence • ω1S/2π~350-500 MHz

Andy Smith and Bjoern Corzilius

1H source

13Csource

1H match

1H tune

13C match

13C tune

13C trap 13C trap

1H trap 1H trap

1H balance

13C balance

resonatorProbe

μ-waves

waveguide

12.7 mm

2.7 mm

Fixedplunger

helix

R.F. leads

sample

waveguide

Adjustableplunger

(a)

(b)

(c)

5 mm

250 GHz Amplifier for Pulsed DNP

9.6 T Magnet

Electron Gun

HV Modulator Transmission Line

Solid State Source 30mW 248 GHz – 258 GHz

Heterodyne Frequency Detector

Control System

Gyrotron Amplifier

Nanni, PRL 111,235101 (2013)








NEW

NEW

DNP Outline

Collaborators

Polarizing AgentsJoe WalishOlesya HazeTim SwagerPaul Tordo

Overhauser DNPCody Can

Bjoern CorziliusFred Mentink-Vigier

Marc CaporiniMelanie RosayWerner MaasShimon Vega

GyrotronsEmilio Nanni

Sudheer JawalMichael Shapiro

Paul Woskow

Richard Temkin

DNPCody Can

Bjoern CorziliusEugenio DavisoJennifer MathiesVlad Michaelis

Qing Zhe NiAndy SmithJoe Walish

Marc CaporiniMelanie RosayWerner Maas

National Institute of Biomedical Imaging and Bioengineering

Thank you for

your attention!

Documents

High Frequency Dynamic Nuclear Polarizationwinterschool.mit.edu/sites/default/files/documents/... · 2016-01-10 · Temperature and Field Dependence 1 10 100 300 0.01 0.1 100 Temperature