esr_basics_2_2007.ppt

An introduction to Electron Spin Resonance (ESR), November 7, 2007

An Introduction to Electron Spin Resonance (ESR)

Boris Dzikovski, ACERT, Cornell University

• The application field• The basic ESR experiment.• Some theoretical background.• Nitroxide spin labels.• Some examples for extraction of parameters of molecular dynamics from ESR spectra• Site directed spin labeling (SDSL)• ESR distance measurements


ESR is a spectroscopic technique that detects chemical species that have unpaired electrons :

• Transition metal ions and complexes Mn2+, Cu2+, Gd 3+ etc.• Simple inorganic compounds: O2 , NO, NO2 ….• Short-lived intermediate radicals OH, H, F etc. in kinetics study• Defects in crystals • Electrons trapped in radiation damaged sites • Stable organic radicals • Triplet states• Biological applications:• Paramagnetic cofactors: iron sulfur, copper proteins• Free radicals of biological origin and their spin-trapping products

• Spin-labeling

Energy-level diagram for two spin states as a function of applied field H. This represents the simplest ESR transition (e.g., free electrons).“Allowed” EPR transitions occur when Ms = 1 (Ms is the magnetic spin quantum number of the spin state).The equation describing the absorption (or emission) of microwave energy between two spin states is

E h gH where: E is the energy difference between the two spin statesh is Planck’s constant is the microwave frequencyg is the Zeeman splitting factor (2.0023 for free electron) is the Bohr magnetonH is the applied magnetic field.


H


RelaxationEvolution of a spin system is describedby Bloch equations:

T1- spin-lattice or longitudinal relaxation timeT2- spin-spin or traverse relaxation time

When properly integrated, the Bloch equations will yield the X', Y', and Z components of magnetization as a function of time.

Stationary solution in the rotating frame gives a lorentzian line 20

22

22

)(11)(

HHTTHF

))(21exp(

2)( 2

02

222 HHTTHF

Gaussian line = inhomogeneous broadening

ESR linewidth: HkT e '

2

112

'2 2

111TTT

)/(1076.1 7 Gsrade

k=1 Lorentz

2lnk Gauss

Mx’, My’ Mz – magnetization components in the rotating frame

0=eH0 – the Larmor Frequency


ESR and NMR are very different methods!

electron proton ratio

Rest mass me =9.1094*10-28 g mp =1.6726*10-24 g 5.446*10-4

Charge e=-4.80286*10-10ESU e=4.80286*10-10ESU -1

Angular momentum h/4 h/4 1

Magnetic dipole moment

S=-ge eSge= 2.002322

me=eh/4mec =9.274*10-21 erg/G

S=-gN NSgN= 5.5856

mN=eh/4mNc =

5.0504*10-24 erg/G

1836.12

Frequency: Factor 1000 larger in EPR ! (GHz instead of MHz)Coupling strength: Factor 1 000 000 larger in EPR ! (MHz instead of Hz)Relaxation Times: Factor 1000 000 smaller in EPR ! (ns instead of ms)= much higher techniqual requirements, but unique sensitivity to molecular motion

Sensitivity : Factor 1 000 000 better than in NMR !! (1nM instead of 1mM ) An ideal case, though


The Basic ESR Experiment (conventional ESR)

Source Circulator Detector

electromagnet Modulation coils Resonator (cavity)


The Basic ESR Experiment (conventional ESR)

•ESR is done from 1 to 300+GHz [30mT-10T or 30cm-1mm], up to 2000+ GHzMachines are classified according to their source frequency : Commonly used X-band at 9.5 GHzL (1.5), S (3.0), C (6.0), Ku (17), K (23), Q (36), V (50), W (95), D(140), G(180)

•Field modulation is used to encode the spectrum [1st derivative lineshape]

•Use microwave transmission lines

•Do spectroscopy with a few microwatts to a few milliwatts of power•Solid state [Gunn diode or DRO] or tube [klystron] sources

•Temperatures from 4K (heme and non-heme iron) to 310K+ (in vivo/vitro)

• Sensitivity : Increases as (frequency)2, but limited by sample size, field homogeneity and component construction problems. Practically (at X-band): detect 1011 spins, a detectable concentration of ~10-9M.

Unlike NMR a large proportion of machines are still 'cw'. That is they do not use pulsed detection methods


Field modulation


A commercial 9GHz system


Commercial 95GHzSpectrometer (3T)


The g-factor:E = h = gH

The field at each spin influenced by local magnetic fields, not just the external field : Heft = H + Hlocal so Heff = (1-s)H = (g/ge)H

-This field is induced by H, and so depends on the external field H -g is an effective Zeeman factor, shifted from the electron g-factor, ge -The shift in g is akin to the chemical shift of NMR -The local induced field comes from the orbital motion of electrons, spin-orbit coupling mixes J, L and S and shifts g, the shift can can be g<2 or g>2. g is thus characteristic of different electronic structures and is also known as the Landé splitting factor:

Light atoms, i.e.'organic' and first row transition metals with a single unpaired electron can have g close to 2.0 Heavier atoms, and molecules or atoms with more than one unpaired electron can have g-values very different from 2


g-value Flavin semiquinone, ubiquinone, ascorbate, etc

2.0030 - 2.0050

Nitroxide spin labels and traps 2.0020 - 2.0090

sulphur radicals : S-S, S-H 2.02 - 2.06 MoV (in aldehyde oxidase) 1.94 Cu2+ 2.0 - 2.4 Fe3+ (low spin) 1.4 - 3.1 Fe3+ (high spin) 2.0 - 10

g-values for some biologically important paramagnetic compounds


The unpaired electron, which gives us the EPR spectrum, is very sensitive to local fields in its surroundings. Local fields arising from magnetic nuclei are permanent and independent of H. Interaction with neighboring nuclear magnetic dipoles gives the nuclear hyperfine interaction and hyperfine splitting ACorresponds to the NMR coupling constant J A splittings are independent of the external field.For several equivalent nuclei n, (2nMIM + 1) transitions are observed for a nucleus M with a spin I The relative intensities are given by Pascal's triangle for I = ½

11 1

1 2 11 3 3 1

1 4 6 4 11 5 10 10 5 1

1 6 15 20 15 6 11 7 21 35 35 21 7 1

A - the hyperfine splitting


I=1/2, 2I+1=2

I=1, 2I+1=3

Organic radicals in the liquid phase

Cyclooctatetraen anion

Observation of the 1:8:28:56:70:56:28:8:1

spectrum shows that eightprotons are equivalent

Butadien ion in liquid NH3

Two sets of equivalent protons: 2 and 4

Pyrazine anion

Na+ is the counterion

K+ is the counterion


The figures are taken from the textbook by Wertz&Bolton


Anisotropy in g and A

Many measurements are made in the solid state in EPR spectroscopy.

The ability of EPR to obtain useful information from amorphous (glassy) and polycrystalline (powders) as well as from single crystal materials has attracted much biology and biochemistry research Usually : gX, gY, gZ are not all equal, so g is anisotropic. Same for AX, AY, AZ.

For EPR the local symmetry at an unpaired electron center is categorised as : •Cubic. If x = y = z is cubic (cubal, octahedral, tetrahedral) No anisotropy in g and A. •Uniaxial (Axial). If x = y, and z is unique. Linear rotation symmetry (at least 3-fold). Two principal values each for g and A. For an arbitrary orientation:

•Rhombic. Three unequal components for g and A For an arbitrary orientation:

22222 cossin IIggg

222222222 cossinsincossin ZZYYXX gggg


gx=2.0091, gy=2.0061, gz=2.0023The field shift between the X- and Z- orientations is

H=h/gx- h/gz hg/4~11G


gx=2.0091, gy=2.0061, gz=2.0023I=1/2, Ax= 6.2, Ay = 6.3, Az=33.6


gx=2.0091, gy=2.0061, gz=2.0023I=1, Ax= 6.2, Ay = 6.3, Az=33.6


Powder and glass spectra S=1/2, I=0, gx=gy<>gz Axially symmetric g-factor

2/12222 ]sincos[

ggh

ghH IIeff

r

is the angle between a given symmetry axis and themagnetic field direction

The given solid angle is defined to be the ratio of the surface area A to the total surface area on the sphere: A/4r2

d2r2sind4r2sind ddHHP sin)(

ddH

HP/

sin)(

cos)()sincos()( 22

2/32222

gg

ggh

HPII

II

cos)(1)( 223

ggHhHP

IIr


Axial Lineshape Rhombic Lineshape


EPR Middle-Earth

Q-band ESR spectrum of molecularoxygen at reduced pressure

5000 15000 G10000The rotational angular momentum, which is quenched in the liquid or solid phases couples strongly to the electronic spin and orbital angular momenta…

ESR signals around us

EPR dosimetry:

Toothpaste Human hair


Determination of the accumulated radiationdose by ESR of tooth enamel

An introduction to Electron Spin Resonance (ESR),

Nitroxide spin labels

NO

NO

N

O

CH3

CH3

CH3

H3C

CH3

H3CH

O

The g- and A-tensor frame for anitroxide radical



gx=2.0091, gy=2.0061, gz=2.0023I=1, Ax= 6.2, Ay = 6.3, Az=33.6

9.4 GHz



Angular averaging in the case of S=1/2, I=1, gx=2.0089, gy=2.0061, gz=2.0027, Ax= 5.2, Ay = 5.2, Az=31.0, X-Band


component I=+1is spread over A- hg/4

component I=0is spread over hg/4

component -1is spread over A+ hg/4

The figures are from the monograph by Kuznetsov


High field EPR spectroscopy is the g-resolved spectroscopy,the regions corresponding different orientations of the magneticaxis relative to the external magnetic field do not overlap


gx=2.0091, gy=2.0061, gz=2.0023I=1, Ax= 6.2, Ay = 6.3, Az=33.6

170 GHz



Nitroxyl tumbling correlation timeAs the molecule tumbles, the smaller splitting for mI = 0 is averaged more effectively than the larger splittings, which causes differences in the linewidths of the three hyperfine lines:


Nitroxyl Lineshapes

As the tumbling correlation time decreases, the extent of averaging of anisotropic features increases and the spectrum approaches the 3-line signal that is characteristic of rapid tumbling.In the motional narrowing region, the dependence of the width of an individual hyperfine line on the nuclear spin state (mI) can be expressed as

2 )( ImCmBAmB II

X-band

Rotation correlation times between 10-11 and 10-6 are detectable by ESR


)1(I)0(I

)1(I)0(I

21B

The parameters B and C are related to peak-to-peak amplitudes, I(mI) by:

2

)1(I)0(I

)1(I)0(I

21C

The high-field line has mI = -1. Tumbling correlation times are calculated from B and C using

1

o

2

o B1

8b

g32C

and

Where

1

o

oB1b

15B4

og32B

)ggg(31g zyxo

o

o gB

))(5.0( yxz ggg

))AA(5.0A(32b yxz

Bo is the peak-to-peak width of the center line Hyperfine values (A) are in radians/s The calculation assumes isotropic tumbling

Calculation of tumbling times in the case of fast isotropic tumbling


NO

OH

Sample Calculation

gx = 2.0094, gy = 2.0059, gz = 2.0023

Ax = 218x106, Ay = 222.5x106, Az = 2103x106

rad/s

I(+1) = 13.5, I(0) = 16.4, I(-1) = 3.4 (arbitrary units)

Bo = 3.52 Gauss = 9.274x10-21 erg/G= 9.2449x109 s-1 h=6.626x10-27 erg s = 2.1x10-9 s from B or = 2.3x10-9 s from C

The disagreement is an indication of the approximate nature of this calculation.

4-OH-TEMPO (tempol) in 9:1 glycerol:water

Determination of microviscosity:kTV (Stocks-Einstein)

Extremely useful in oversaturated/overcooled disperse systems.Example: testing photographic materials


g- and A- tensors are sensitive to the local polarity

TEMPO in Emulsion: toluene/SDS/water

NO

OHgx gy gz giso Ax Ay Az Aiso

Toluene 2.00986 2.00626 2.00222 2.00617 6.2 7.0 34.3 15.6

Water/glyc 2.00878 2.00604 2.00215 2.00565 6.9 7.9 37.4 17.4


TEMPO in the LQ phase of DLPC

Partially A-resolved g-resolved spectra


Orientational resolution of HF ESR for nitroxide spin labels

One of the main virtues of HF ESR over ESR at conventional microwave frequency is the excellent orientational resolution for nitroxide spin labels. At HF, once motion is discernable in the spectrum, one can discern about which axis the motion occurs.

Spin labeled fatty acids in solid cyclodextrins

COOHNOO

COOH

O NO

NOOC

O


Z-rotation vs. slow motion

Averaging real tensor componentsgxx, gyy, gzz, Axx, Ayy, Azz

Averaging effective tensor components

(gxx+ gyy)/2, (gxx+ gyy)/2, gzz (Axx+ Ayy)/2, (Axx+ Ayy)/2 Azz

X-rotation



gxx,, (gyy+ gzz)/2, (gyy+ gzz)/2, Axx, (Ayy+ Azz)/2, (Ayy+ Azz)/2

Diffusion tilt angle Y-rotation



(gxx+ gzz)/2, gyy, (gxx+ gzz)/2, (Axx+ Azz)/2, Ayy, (Axx+ Azz)/2


O O

O O

O

P

O

O O

O

N

O

ONO

ONO

zR

CC

C CH2CH2

CH2 CH2 N CH3

CH3

CH3

_ +

xm

zm

Side view Upper view

ym

16-PC

O O

O O

O

P

O

O O

N

O

CC

CH CH2 CH2

CH2 CH2

N

H3C CH3

_

+

xm

ymzR

zd

DPPTC

ONO

zd

xm

ym

zm

CSL

Z-ordering X-orderingY-ordering

Lipid spin labels


ESR is one of the most powerful tools in lipid research

Phase state of lipids

Interaction of lipid with proteins, formation of lipoproteids, boundary lipid etc.

Domains in model and biological membranes

Diffusion studies in the membrane phase

Polarity profiles in membranes

Membrane permeation profiles for oxygen and paramagnetic ions

ESR on aligned membranes

Simulation of angular dependent spectra is much freer of ambiguity, compared to vesicles

Spin-labeled gramicidin A in DPPC, 220 C

Aligned membrane Vesicles

Application of aligned membranes allows extracting information on relative orientation of diffusion and magnetic axes, which can not be obtained from vesicles



6 0 5 0 0 6 0 6 0 0 6 0 7 0 0 6 0 8 0 0 6 0 9 0 0 6 1 0 0 0 6 1 1 0 0

M O M D

4 5 0

9 0 0

0 0

H 0 , G

Spin labeled Gramicidin A in DPPC at 170 GHz

gx=2.0091, gy=2.0061, gz=2.0023I=1, Ax= 6.2, Ay = 6.3, Az=33.6

All orientations of the membrane normal relative to the magnetic field are averaged in vesicles:

NO

For a macroscopically disordered sample the orientation of the nitroxidemoiety manifests itself as a result of anisotropic molecular motion around the principal axis of the molecular frame

NO

OCO

C

OHO

O

NO

n n

X Z

9 GHz 170 GHz

MOMD: microscopic order – macroscopic disorder. An important case in biology


Spin labeling. Peptides and proteins

R N

OOH

N

HOO

+DCC O

NO

R

OO

N O

Nitroxides are introduced into proteins as reporter groups to provide information about local environment, overall tumbling rate of the protein or/and segmental mobility, accessibility of the labeling site for polar/non-polar molecules, distance measurements to other spin labels, co-factors, membrane surface….

Labeling of the hydroxyl group

NOCH2SSO2CH3Protein SH + S CH2

NOSProtein

MTSL spin label is cysteine specific.

SDSL = site directed spin labeling is introducing cysteines into the protein molecule by point mutations with following MTSL labeling.Cysteine mapping of the protein molecule.


T4 lysozyme – an example of successful EPR mapping

Multifrequency approach: high field EPR (250 GHz) spectra are insensitive to the slow overall tumbling motion of the protein and indicative of the internal motionThe 9 GHz spectra significantly affected by the overall tumbling andless sensitive to the internal dynamics.

Multifrequency Analysis

R (s-1)

Note: τR = (6R)-1

Time scale



Oxygen Accessibility

W. L. Hubbell, H. S. Mchaourab, C. Altenbach, and M. A. Lietzow, Structure 4, 779-783 (1996).

Oxygen accessibility and probe mobility were measured as a function of sequence number for spin labels attached to T4 lysozyme (T4L) and cellular retinol binding protein (CRBP). The correlation between the two parameters indicates that the most mobile sites are also the most oxygen accessible.The repeat period of about 3.6 for T4L is consistent with the -helical structure of this segment of the protein.


ESR distance measurements

Dipole-dipole interaction between two spins: 521

321 ))((3

rrr

rWdipolar

)))((3

( 532

jk

jkkjkj

jk

kjBjjDD r

rSrSr

SSggH

)1cos3(1 222

3 Bejk

DD gr

H

Proportional to (interspin distance)-3 angular dependent splitting.Averaging over all orientations gives the Pake Doublet:


Some modern pulse EPR techniques (DQC, DEER) can cancel out all interactions resulting in an EPR spectrum except the dipole interaction in spin pairs

Example: spin labeled Gramicidin A

3/2 re

dipolar, MHz,

2/][]Å[

102.53

4

MHzr dipolar

Å.930Interspin distance=


DQC-EPR ruler:

G-CC-GA-UG-CC-GU-AG-CA-UU-AG-CG-CC-GC-GU-AA-UC-GG-CC-GG-CU-AG-CU-AU-AC-G

(O*N) -U5'

3'

U-(N*O)3'5'

G-CC-GA-UG-CC-GU-AG-CA-UU-AG-CG-CC-GC-GU-AA-UC-GG-CC-GG-CU-AG-CU-AU-AC-G

(O*N) -U5'

3'

U-(N*O)3'5'

10 20 7030 40 50 60 1009080

DQC RULER

Å

Location of mobile domains in a protein complex using DQC-ESR:

esr_basics_2_2007.ppt

Documents

t1 spin

spin statesh

spin system

esr spectrasite

nitroxide spin labels

magnetic spin quantum

simplest esr transition

han introduction