1. 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

2. An introduction to Electron Spin Resonance (ESR), November 7, 2007 ESR is a spectroscopic technique that detects chemical species that have unpaired electrons : Transition metal ions and complexes Mn 2+, Cu 2+, Gd 3+ etc. Simple inorganic compounds: O 2, NO, NO 2 …. 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

3. 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  M s  = 1 (M s 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  g  H where:  E is the energy difference between the two spin states h is Planck’s constant  is the microwave frequency g is the Zeeman splitting factor (2.0023 for free electron)  is the Bohr magneton H is the applied magnetic field. An introduction to Electron Spin Resonance (ESR), November 7, 2007 H

4. Relaxation Evolution of a spin system is described by Bloch equations: T 1 - spin-lattice or longitudinal relaxation time T 2 - 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 Gaussian line = inhomogeneous broadening ESR linewidth: k=1 Lorentz Gauss M x’, M y’ M z – magnetization components in the rotating frame  0 =  e H 0 – the Larmor Frequency

5. An introduction to Electron Spin Resonance (ESR), November 7, 2007 ESR and NMR are very different methods! electronprotonratio Rest massm e =9.1094*10 -28 gm p =1.6726*10 -24 g5.446*10 -4 Chargee=-4.80286*10 -10 ESUe=4.80286*10 -10 ESU Angular momentum h/4  1 Magnetic dipole moment  S =-g e  e S g e = 2.002322 m e =eh/4  m e c = 9.274*10 -21 erg/G  S =-g N  N S g N = 5.5856 m N =eh/4  m N c = 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

6. An introduction to Electron Spin Resonance (ESR), November 7, 2007 The Basic ESR Experiment (conventional ESR) Source CirculatorDetector electromagnetModulation coilsResonator (cavity)

7. An introduction to Electron Spin Resonance (ESR), November 7, 2007 The Basic ESR Experiment (conventional ESR) ESR is done from 1 to 300+GHz [30mT-10T or 30cm-1mm], up to 2000+ GHz Machines are classified according to their source frequency : Commonly used X-band at 9.5 GHz L (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 [1 st 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 10 11 spins, a detectable concentration of ~10 -9 M. Unlike NMR a large proportion of machines are still 'cw'. That is they do not use pulsed detection methods

8. An introduction to Electron Spin Resonance (ESR), November 7, 2007 Field modulation

9. An introduction to Electron Spin Resonance (ESR), November 7, 2007 A commercial 9GHz system

10. An introduction to Electron Spin Resonance (ESR), November 7, 2007 Commercial 95GHz Spectrometer (3T)

11. An introduction to Electron Spin Resonance (ESR), November 7, 2007 The g-factor:  E = h  = g  H The field at each spin influenced by local magnetic fields, not just the external field : H eft = H + H local so H eff = (1-s)H = (g/g e )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, g e  -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. 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

12. An introduction to Electron Spin Resonance (ESR), November 7, 2007 g-value Flavin semiquinone, ubiquinone, ascorbate, etc 2.0030 - 2.0050 Nitroxide spin labels and traps2.0020 - 2.0090 sulphur radicals : S-S, S-H2.02 - 2.06 Mo V (in aldehyde oxidase)1.94 Cu 2+ 2.0 - 2.4 Fe 3+ (low spin)1.4 - 3.1 Fe 3+ (high spin)2.0 - 10 g-values for some biologically important paramagnetic compounds

13. An introduction to Electron Spin Resonance (ESR), November 7, 2007 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 A Corresponds to the NMR coupling constant J A splittings are independent of the external field. For several equivalent nuclei n, (2n M I M + 1) transitions are observed for a nucleus M with a spin I The relative intensities are given by Pascal's triangle for I = ½ 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 A - the hyperfine splitting

14. An introduction to Electron Spin Resonance (ESR), November 7, 2007 I=1/2, 2I+1=2 I=1, 2I+1=3

15. Organic radicals in the liquid phase Cyclooctatetraen anion Observation of the 1:8:28:56:70:56:28:8:1 spectrum shows that eight protons are equivalent Butadien ion in liquid NH 3 Two sets of equivalent protons: 2 and 4 Pyrazine anion Na + is the counterion K + is the counterion An introduction to Electron Spin Resonance (ESR), November 7, 2007 The figures are taken from the textbook by Wertz&Bolton

16. An introduction to Electron Spin Resonance (ESR), November 7, 2007 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 : g X, g Y, g Z are not all equal, so g is anisotropic. Same for A X, A Y, A Z. 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:

17. An introduction to Electron Spin Resonance (ESR), November 7, 2007 g x =2.0091, g y =2.0061, g z =2.0023 The field shift between the X- and Z- orientations is  H=h /g x  - h /g z   h  g/4  ~11G

18. An introduction to Electron Spin Resonance (ESR), November 7, 2007 g x =2.0091, g y =2.0061, g z =2.0023 I=1/2, A x = 6.2, A y = 6.3, A z =33.6

19. An introduction to Electron Spin Resonance (ESR), November 7, 2007 g x =2.0091, g y =2.0061, g z =2.0023 I=1, A x = 6.2, A y = 6.3, A z =33.6

20. An introduction to Electron Spin Resonance (ESR), November 7, 2007 Powder and glass spectra S=1/2, I=0, g x =g y <>g z Axially symmetric g-factor is the angle between a given symmetry axis and the magnetic 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/ 4  r 2 d  2  r 2 sin  d  4  r 2  sin  d 

21. An introduction to Electron Spin Resonance (ESR), November 7, 2007 Axial LineshapeRhombic Lineshape

22. An introduction to Electron Spin Resonance (ESR), November 7, 2007 EPR Middle-Earth

23. Q-band ESR spectrum of molecular oxygen at reduced pressure 500015000 G10000 The 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 An introduction to Electron Spin Resonance (ESR), November 7, 2007 Determination of the accumulated radiation dose by ESR of tooth enamel

24. An introduction to Electron Spin Resonance (ESR), Nitroxide spin labels The g- and A-tensor frame for a nitroxide radical An introduction to Electron Spin Resonance (ESR), November 7, 2007

25. An introduction to Electron Spin Resonance (ESR), g x =2.0091, g y =2.0061, g z =2.0023 I=1, A x = 6.2, A y = 6.3, A z =33.6 9.4 GHz An introduction to Electron Spin Resonance (ESR), November 7, 2007

26. An introduction to Electron Spin Resonance (ESR), Angular averaging in the case of S=1/2, I=1, g x =2.0089, g y =2.0061, g z =2.0027, A x = 5.2, A y = 5.2, A z =31.0, X-Band An introduction to Electron Spin Resonance (ESR), November 7, 2007 component I=+1 is spread over  A- h  g/4  component I=0 is spread over h  g/4  component -1 is spread over  A+ h  g/4  The figures are from the monograph by Kuznetsov

27. An introduction to Electron Spin Resonance (ESR), High field EPR spectroscopy is the g-resolved spectroscopy, the regions corresponding different orientations of the magnetic axis relative to the external magnetic field do not overlap An introduction to Electron Spin Resonance (ESR), November 7, 2007

28. g x =2.0091, g y =2.0061, g z =2.0023 I=1, A x = 6.2, A y = 6.3, A z =33.6 170 GHz An introduction to Electron Spin Resonance (ESR), November 7, 2007

29. Nitroxyl tumbling correlation time As the molecule tumbles, the smaller splitting for m I = 0 is averaged more effectively than the larger splittings, which causes differences in the linewidths of the three hyperfine lines:

30. An introduction to Electron Spin Resonance (ESR), November 7, 2007 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 (m I ) can be expressed as X-band Rotation correlation times between 10 -11 and 10 -6 are detectable by ESR

31. An introduction to Electron Spin Resonance (ESR), November 7, 2007 The parameters B and C are related to peak-to-peak amplitudes, I(m I ) by: The high-field line has m I = -1. Tumbling correlation times are calculated from B and C using and Where  B o 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

32. An introduction to Electron Spin Resonance (ESR), November 7, 2007 Sample Calculation g x = 2.0094, g y = 2.0059, g z = 2.0023 A x = 2  18x10 6, A y = 2  22.5x10 6, A z = 2  103x10 6 rad/s I(+1) = 13.5, I(0) = 16.4, I(-1) = 3.4 (arbitrary units)  B o = 3.52 Gauss  = 9.274x10 -21 erg/G = 9.2449x10 9 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: (Stocks-Einstein) Extremely useful in oversaturated/overcooled disperse systems. Example: testing photographic materials

33. An introduction to Electron Spin Resonance (ESR), November 7, 2007 g- and A- tensors are sensitive to the local polarity TEMPO in Emulsion: toluene/SDS/water g x g y g z g iso A x A y A z A iso 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

34. An introduction to Electron Spin Resonance (ESR), November 7, 2007 TEMPO in the LQ phase of DLPC Partially A-resolvedg-resolved spectra

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

36. An introduction to Electron Spin Resonance (ESR), November 7, 2007 Z-rotation vs. slow motion Averaging real tensor components g xx, g yy, g zz, A xx, A yy, A zz Averaging effective tensor components (g xx + g yy )/2, (g xx + g yy )/2, g zz (A xx + A yy )/2, (A xx + A yy )/2 A zz

37. X-rotation An introduction to Electron Spin Resonance (ESR), November 7, 2007 Averaging effective tensor components g xx,, (g yy + g zz )/2, (g yy + g zz )/2, A xx, (A yy + A zz )/2, (A yy + A zz )/2

38. Diffusion tilt angleY-rotation An introduction to Electron Spin Resonance (ESR), November 7, 2007 Averaging effective tensor components (g xx + g zz )/2, g yy, (g xx + g zz )/2, (A xx + A zz )/2, A yy, (A xx + A zz )/2

39. An introduction to Electron Spin Resonance (ESR), November 7, 2007 Z-orderingX-ordering Y-ordering Lipid spin labels

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

41. ESR on aligned membranes Simulation of angular dependent spectra is much freer of ambiguity, compared to vesicles Spin-labeled gramicidin A in DPPC, 22 0 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 An introduction to Electron Spin Resonance (ESR), November 7, 2007

42. Spin labeled Gramicidin A in DPPC at 170 GHz

43. g x =2.0091, g y =2.0061, g z =2.0023 I=1, A x = 6.2, A y = 6.3, A z =33.6 All orientations of the membrane normal relative to the magnetic field are averaged in vesicles: For a macroscopically disordered sample the orientation of the nitroxide moiety manifests itself as a result of anisotropic molecular motion around the principal axis of the molecular frame n n XZ 9 GHz 170 GHz MOMD: microscopic order – macroscopic disorder. An important case in biology

44. An introduction to Electron Spin Resonance (ESR), November 7, 2007 Spin labeling. Peptides and proteins 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 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.

45. An introduction to Electron Spin Resonance (ESR), November 7, 2007 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 motion The 9 GHz spectra significantly affected by the overall tumbling and less sensitive to the internal dynamics.

46. Multifrequency Analysis R (s -1 ) Note: τ R = (6R) -1 Time scale An introduction to Electron Spin Resonance (ESR), November 7, 2007

47. 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.

48. An introduction to Electron Spin Resonance (ESR), November 7, 2007 ESR distance measurements Dipole-dipole interaction between two spins: Proportional to (interspin distance) -3 angular dependent splitting. Averaging over all orientations gives the Pake Doublet:

49. An introduction to Electron Spin Resonance (ESR), November 7, 2007 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 dipolar, MHz, Interspin distance=

50. An introduction to Electron Spin Resonance (ESR), November 7, 2007 DQC-EPR ruler: Location of mobile domains in a protein complex using DQC-ESR: