Introduction to Biomolecular Electron Paramagnetic Resonance Theory. E.C. Duin. Wilfred R. Hagen. Spectral Simulations. EPR, the Technique.

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1 Introduction to Biomolecular Electron Paramagnetic Resonance Theory E.C. Duin Wilfred R. Hagen Paper: EPR spectroscopy as a probe of metal centres in biological systems (2006) Dalton Trans Book: Biomolecular EPR Spectroscopy (2009) Fred Hagen completed his PhD on EPR of metalloproteins at the University of Amsterdam in 1982 with S.P.J. Albracht and E.C. Slater. 1 3 EPR, the Technique. Molecular EPR spectroscopy is a method to look at the structure and reactivity of molecules. EPR is limited to paramagnetic substances (unpaired electrons). When used in the study of metalloproteins not the whole molecule is observed but only that small part where the paramagnetism is located. This is usually the central place of action the active site of enzyme catalysis. Sensitivity: 10 μm and up. Naming: Electron paramagnetic resonance (EPR), electron spin resonance (ESR), electron magnetic resonance (EMR) Spectral Simulations The book Biomolecular EPR spectroscopy comes with a suite of programs for basic manipulation and analysis of EPR data which will be used in this class. Isotropic Radicals Simple Spectrum Hyperfine Spectrum EPR File Converter Single Integer Signal GeeStrain-5 Visual Rhombo 2 EPR Editor 4 1

2 Discovery A Free Electron in a Magnetic Field In 1944, E.K. Zavoisky discovered magnetic resonance. Actually it was EPR on CuCl 2. E.K. Zavoisky s first EPR system First EMR on CuCl 2.2H 2 O 133MHz 5 An electron with spin S = ½ can have two orientations in a magnetic field B 0 labeled by m S = +½ or m S = ½. The unpaired electron will have a state of lowest energy when the moment of the electron is aligned with the magnetic field and a state of highest energy when aligned against the magnetic field. 7 EPR Theory A Free Electron in Vacuo A Free Electron in a Magnetic Field Free, unpaired electron in space: electron spin - magnetic moment 6 The energy of each orientation is the product of µ and B 0. For an electron µ = m s g e β, where β is a conversion constant called the Bohr magneton and g e is the spectroscopic g-factor of the free electron and equals ( 2.00). Therefore, the energies for an electron with m s = +½ and m s = -½ are, respectively: ½ g e βb 0 and -½ g e βb 0 8 2

3 A Free Electron in a Magnetic Field Spin-orbit Coupling The electronic-zeeman energies are E = m S gβb Resonance condition: hν = g e βb 0 +½: E = +½g e βb 0 When the electron is bound to one, or more nuclei, then a virtual observer on the electron would experience the nucleus (nuclei) as an orbiting positive charge producing a second magnetic field, δb, at the electron. -½: E = -½g e βb 0 hν = g e β(b e + δb) The electron can change orientation by absorbing electromagnetic radiation which energy should exactly equal the state energy difference ΔE, and this defines the resonance condition: E = hν = g e βb 0 9 Since only the spectrometer value of B is known: hν = (g e + δg)βb = gβb The quantity g = g e + δg contains the chemical information on the nature of the bond between the electron and the molecule, the electronic structure of the molecule. The value of g can be taken as a fingerprint of the molecule. 11 A Free Electron in a Magnetic Field Anisotropy hν = g e βb 0 Two fundamental constants: - Planck s constant: h - Bohr magneton: β Two experimental parameters: - Microwave frequency: ν - Magnetic field: B 0 Anisotropy: the fact that molecular properties, such as δg are angular dependent and reflect the 3D electronic structure of the paramagnet. A constant of proportionality: g-value Property of matter, for the free electron: g = g e = Example: compound with axial paramagnetic anisotropy. This will have a different dg-value for different orientations dependent on the alignment of B 0 along the z-axis or the y- or x-axes. 12 3

4 Powder Spectrum A sample of realistic size consists of randomly oriented molecules, resulting in a socalled powder spectrum. In the example of the compound with axial paramagnetic anisotropy, the spectrum has axial EPR absorption. (Higher chance of having the B- vector anywhere in the xy-plane than parallel to the z-axis.) Angular Dependency of g-value Inclusion of the angular terms into the resonance equation gives: hν = g θ, φ βb 0 A spin Hamiltonian that considers any arbitrary orientation of B relative to g is given by: H = βb T g S With S being the Pauli spin operator vector with individual components S x, S y, and S z Angular Dependency of g-value Angular Dependency of g-value B can be aligned along any of the principle g tensor axes and the individual components of B are defined in terms of the polar angles (θ, φ). B x = B sinθ cosϕ, B y = B sinθ sinϕ, and B z = B cosθ Defining the orientation of the magnetic field (a vector) with respect to the coordinates of the molecule (and vice versa). Two polar angles, θ and ϕ, where θ is the angle between the vector B and the molecular z-axis, and ϕ is the angle between the projection of B onto the xy-plane and the x-axis. 14 Filling in these values provides a more detailed matrix representation of the spin Hamiltonian equation: H = β B x B y B z g xx g yy g zz S x S y S z 16 4

5 Angular Dependency of g-value Combining with the polar angles equations for the individual components of B: H = β(bsinθcosφ g xx S x + Bsinθsinφ g yy S y + Bcosθ g zz S z ) The effect of the S x, S y, S z operators can be represented by the 2 2 Pauli spin matrices quantized in units of ħ as: S x = , S y = i i 0, S z = Angular Dependency of g-value For resonance absorption to occur: E 1 E 2 = hν = g θ, φ βb 0 As a result the value of g(θ, φ) now becomes: g θ, φ = g 2 xx sin 2 θcos 2 φ + g 2 yy sin 2 θsin 2 φ + g 2 zz cos 2 θ This equation gives the effective anisotropic g value for any orientation (θ, φ) with respect to the applied magnetic field B Angular Dependency of g-value Angular Dependency of g-value The matrix of the Hamiltonian has the form: For axial spectra: g ax θ = g 2 xy sin 2 θ + g 2 z cos 2 θ H = β 1 2 B g zz cosθ g xx sinθcosφ + ig yy sinθsinφ g xx sinθcosφ ig yy sinθsinφ g zz cosθ The two resulting eigenvalues are: E 1 = 1 2 βb g xx 2 sin 2 θcos 2 φ + g 2 yy sin 2 θsin 2 φ + g 2 zz cos 2 θ E 2 = 1 2 βb g xx 2 sin 2 θcos 2 φ + g 2 yy sin 2 θsin 2 φ + g 2 zz cos 2 θ 18 Plot of the angle θ and the axial g-value versus the resonance field (g z = and g xy = 2.002, ν = 9500 MHz) 20 5

6 Line Shape of EPR Spectra Correlation Between Line Shape and Structure EPR symmetry g and A tensors Molecular point symmetry Isotropic g xx = g yy = g zz A xx = A yy = A zz O h, T d, O, T h, T Axial Rhombic g xx = g yy g zz D 4h, C 4v, D 4, D 2d, D 6h, A xx = A yy A zz C 6v, D 6, D 3h, D 3d, C 3v, D 3 g xx g yy g zz A xx A yy A zz D 2h, C 2v, D 2 Note: g // = g z and g = g xy g-value Correlation Between Line Shape and Structure Two fundamental constants: - Planck s constant: h - Bohr magneton: β For X-band: hν = gβb 0 ν (MHz) g = B (Gauss) Does the shape of the EPR signal, isotropic, axial, or rhombic reflect the symmetry of a coordination site in a metalloprotein? Most of the time the answer is: No! Example: the Cu(II) spectrum of plastocyanin is virtually axial (g x g y ) even when recorded at higher frequency for increased g-value resolution. Crystallographic analysis, however, reveals a highly distorted tetrahedral site essentially with no symmetry at all!

7 S=1/2 Systems Hyperfine Interactions +½: E = +½g e βb 0 -½: E = -½g e βb 0 Additional splitting can be observed in EPR signals: Hyperfine interaction Interaction of the electron spin with the nuclear spin of the metal ion nucleus Super hyperfine interaction Interaction of the electron spin with first coordinate sphere ligands nuclei Resonance condition: E = hν = g e βb 0 For X-band: g = ν (MHz) B (Gauss) 25 Spin-spin interaction Interaction of the electron spin with other electron spins within 10 Å distance. 27 What is this!?! Hyperfine Interactions 26 Interaction of the electron spin (S = ½) with the nuclear spin of the metal ion nucleus (I = ½) Four different situations: Four new energy levels 28 7

8 Hyperfine Interactions With the four new energy levels there are two field positions where the resonance conditions are met: Δm s = 1, Δm I = 0 The signal is in principle split in two. The original, unsplit, peak would have been exactly in the middle of the two hyperfine lines. Quantum Mechanical Description For an isolated system with a single unpaired electron and no hyperfine interaction the only relevant interaction is the electronic Zeeman term, so the spin Hamiltonian is H s = βbβ(sinθcosφ g xx S x + sinθsinφ g yy S y + cosθ g zz S z ) A shorter way of writing this is H s = βb g S Solving this we get the equation we saw earlier for the angular dependency of the g-value g θ, φ = g 2 xx sin 2 θcos 2 φ + g 2 yy sin 2 θsin 2 φ + g 2 zz cos 2 θ Quantum Mechanical Description Quantum Mechanical Description A full quantum mechanical description of the spectroscopic EPR event is not possible due to the complexity of the systems under study. In Biomolecular EPR spectroscopy we use the concept of the spin Hamiltonian. This describes a system with an extremely simplified form of the Schrödinger wave equation that is a valid description only of the lowest electronic state of the molecule plus magnetic interactions. More terms can be added to the Hamiltonian when needed. For hyperfine interactions H s becomes H s = βb g S + S A I where A is the anisotropic hyperfine tensor. For multi-electron (high-spin) systems H s becomes H s = βb g S + S D S where D is the zero-field interaction. H s ψ s = Eψ s With: H s, spin Hamiltonian; y s, the spin functions; E, energy values of the ground state spin manifold. 30 When both are present, both terms will have to be added! 32 8

9 Quantum Mechanical Description These simplified wave equations will sometimes, under strict conditions, give analytical solutions. It is important to realize that a lot of the tools and simulations software used in biomolecular EPR spectroscopy can only be used when certain conditions are met. In most systems we will encounter, we can use these tools without any problem. There are specific cases, however, where we cannot use these tools. Quantum Mechanical Description Using these assumptions the resonance condition becomes hυ = gβb 0 + ham I where A is called the Hyperfine Coupling Constant and m I is the magnetic quantum number for the nucleus. This describes most hyperfine patterns we will encounter. Exceptions can be found for example for Cu-ion spectra (A-values of Gauss) measured at lower frequencies (L-band). In some Cu spectra the g and A tensors are not linear. Other examples are Mn 2+ spectra where D is small Quantum Mechanical Description Hyperfine interaction: H s = βb g S + S A I Hyperfine Interactions How to determine the hyperfine coupling constant A: Interaction with I = 1/2 Assumption 1: the Zeeman interaction is much larger (two orders of magnitude or more) than the hyperfine interaction which can therefore be treated as a perturbation of the larger Zeeman interaction. Assumption 2: Just like the Zeeman interaction, the hyperfine interaction will be anisotropic. It is assumed that g and A are collinear. 34 A A A Interaction with I =

10 Hyperfine Interactions With the four new energy levels there are two field positions where the resonance conditions are met. Hyperfine Interactions Bio ligand atom nuclear spins and their EPR superhyperfine patterns The signal is in principle split in two. The original, unsplit, peak would have been exactly in the middle of the two hyperfine lines Hyperfine Interactions Organic Radicals Effect of hyperfine splitting on anisotropic signals can be very complex Bio transition metal nuclear spin and their hyperfine structure Organic radicals Measured in solution. Fast tumbling motions of the molecules averages the axial anisotropy of the g-factors resulting in the detection of only a narrow isotropic EPR signal with a single g-value, g iso. Line shape is pure isotropic

11 Hyperfine Interactions Since there are 2I + 1 possible values of m I (m I = I, I-1,, 0,,-I+1, -I), the hyperfine interaction terms splits the Zeeman transition into 2I + 1 lines of equal intensity. Hyperfine Interactions Use a stick diagram or Pascal triangle to predict the relative intensities of each line. No interaction I = ½ I = 1 2 lines 3 lines I = 3/2 4 lines I = 2 5 lines Hyperfine Interactions Different patterns with lines with different intensities are obtained when the unpaired electron interacts with more than one nucleus with the same nuclear spin. No interaction 1x I = ½ 2x I = ½ 3x I = ½ Hyperfine Interactions Different patterns with lines with different intensities are obtained when the unpaired electron interacts with more than one nucleus with the same nuclear spin. No interaction 1x I = 1 2x I = 1 3x I = 1 4x I = ½ 42 4x I =

12 Hyperfine Interactions Use a stick diagram or Pascal triangle to predict the relative intensities of each line. Organic Radicals: Localized Note that due to the fact that the OH proton is exchangeable there is no interaction observed. However, since only the α- and β-protons are contributing virtually the same spectrum is generated by making a n-propyl radical (CH 3 CH 2 CH 2 ) or a n-butanyl radical (CH 3 CH 2 CH 2 CH 2 ). Interaction with 4 N atoms with I = 1 results in a spectrum with 9 lines Organic Radicals: Localized Organic Radicals: Localized The unpaired electron density or spin density is close to unity on one particular atom in the molecule. The unpaired electron will not interact to a significant amount for nuclei further than two bonds away from the atom with the unpaired electron. Example: ethanol radical HOCH 2 CH 2 For this ethanol radical you would only expect to see splittings from the protons of the two CH 2 groups. These protons are termed α- and β-protons, counting from the atom with the unpaired electron. Protons that are further away (e.g., the OH proton) will be expected to give a negligible hyperfine coupling constant. 46 The EPR spectrum of the ethanol radical shows a triplet of triplets HO-C(H β ) 2 -C(H α )

13 Organic Radicals: Delocalized The unpaired electron in an orbital that can be delocalized over the whole molecule or a large section. In delocalized radicals, hyperfine interaction affects spinactive nuclei attached to atoms in the α- and β-position with respect to the unpaired electron. Nuclei in identical chemical environments are equivalent. Example: benzene radical anion. Due to the delocalization, the spin density is spread around the whole molecule and all the protons interact with the unpaired electron. In the benzene anion radical all six hydrogen atoms are equivalent and they will cause a split of the EPR signal into a septet. 49 Benzyl Radical The electron is still delocalized but the HOMO has different densities on the different C atoms The two ortho-protons are attached to carbons with the same spin density and their chemical environment is the same hence they are equivalent and will split EPR signal into a 1:2:1 triplet Meta-protons are also equivalent and yield triplet splitting. 51 Organic Radicals: Delocalized Benzyl Radical In the benzene anion radical all six hydrogen atoms are equivalent and they will cause a split of the EPR signal into a septet. The fast rotation across C-C bond linking the aromatic ring to the methylene group makes the two protons H α equivalent hence triplet splitting from this group. The only para-proton will split the signal into a doublet. The EPR spectrum of benzyl radical should thus give a triplet (H α ) of triplets (H ortho ) of triplets (H meta ) of doublets (H para ) resulting in = 54 lines

14 How to Analyze Splitting Patterns How to Analyze Splitting Patterns ii. If the structure of the molecule is available, identify all nuclei with a nuclear spin in the α- and β-position relative to the unpaired electron. Use splitting diagrams to reproduce the splitting pattern and use a Pascal triangle and to determine the relative intensity of the hyperfine lines for each environment. Four of the triplets around 338 mt and mt overlap hence the total number of lines in the spectrum is 48 rather than How to Analyze Splitting Patterns i. Make sure the overall spectrum is symmetrical. If this is not the case you are dealing with more than one paramagnetic species. You have to look for measuring conditions that allow the spectra to be measured with different ratios. If that is possible you could try to isolate each species by a series of subtractions. If this is not possible you will have to try to insulate and analyze both spectra separately. How to Analyze Splitting Patterns iii. To get to the first multiplet (multiplet A), take the distance between the first two lines at the low field (e.g., left side) in the spectrum. Measure out this same distance to detect if there are more lines that belong to this multiplet. Keep in mind that that the multiplet might not be symmetrical due to overlap with lines from other multiplets

15 How to Analyze Splitting Patterns How to Analyze Splitting Patterns iv. To find the second multiplet, measure the distance from the outermost line to the first line which does not form part of multiplet A. This distance corresponds to the hyperfine coupling constant of the next multiplet (labelled B). Just as with multiplet A keep on measuring the same distance towards higher field until all the lines of multiplet B have been identified How to Analyze Splitting Patterns v. Since multiplet B has a larger hyperfine coupling constant A than that of multiplet the hyperfine pattern of multiplet A will be superimposed on each component of multiplet B. vi. Repeat steps 6-9 until all multiplets have been identified. If you somehow get stuck on the left side also start from the right side and try to get to the middle of the spectrum. 58 Solution vs. powder spectra With small molecules in dilute solutions fast tumbling motions averages the anisotropy of the g-factor resulting in the detection of a narrow isotropic EPR signal with one apparent g-value, g iso. In this case the splitting patterns will all have their origin in this central isotropic signal. With large molecules like proteins that show slow tumbling, or molecules in frozen or powder samples, all g-values will be displayed. Now each peak will have its own splitting pattern since the hyperfine interaction A is anisotropic. An average g value can be calculated g av = (g x + g y + g z )/3 for the powder spectra. Note that the g iso obtained at room temperature and the g av obtained on frozen or powder samples can differ slightly due to the influence of solvent at ambient temperatures

16 Hyperfine Splitting on Anisotropic Spectra The hyperfine splitting pattern will be the same for each of the principle g-factors A is anisotropic and therefore the magnitude of the splitting can differ significantly for the different g-factors In some cases the patterns on the different g-factors can even overlap partly or completely making it much more difficult to analyze these patterns. Type Identification - Metals Which redox state is EPR active? Metal Ion Electron Configuration Spin State Fe 2+ d 6 S = 0 (ls) or S = 2 (hs) Fe 3+ d 5 S = 5/2 (hs) Ni 1+ d 9 S = ½ Ni 2+ d 8 S = 0 or S = 1 Ni 3+ d 7 S = ½ Cu 1+ d 10 S = 0 Cu 2+ d 9 S = ½ Prepare different samples: 1) as such 2) reduced (dithionite) 3) oxidized (ferricyanide) How many unpaired electrons? Different spin states! Hyperfine Splitting on Anisotropic Spectra Type Identification - Metals Resolved hyperfine on the g z peak for the Cu nucleus (I = 3/2) Unresolved hyperfine on the g xy peak 62 Has the metal a nuclear spin? Atom Isotope Spin (abundance) V 50, V, 6 (0.25); 51 V, 2 (99.75) Mn Fe 54, 56, 57, (2.119) Co Ni 58, 60, 61, (1.14) Cu 63, Cu, 2 (69.17); 65 Cu, 2 (30.83) Mo 92, 94, 95, 96, 97, 98, Mo, 2 (15.92); 97 Mo, 2 (9.55) W 180, 182, 183, 184, (14.3) Is the signal going to be split into 2 I + 1 lines? In general: The spin orbit coupling parameter is positive for systems with less than half filled outer shells and negative for those with more than half filled shells, which means that the former have g<g e and the latter have g>g e

17 Type Identification - Metals Nickel Ni 1+, d 9 Ni 1+, d 9 Methyl-coenzyme-M reductase g>g e : g xyz = 2.252, 2.073, Hyperfine structure due to N- ligands detectable Nickel Type Identification - Nickel Ni 3+, d 7 Hydrogenase. The iron is low-spin Fe 2+ The signal is due to the nickel g>g e : g xyz = 2.32, 2.24, 2.01 A B C D What if you are not certain about the origin of the spectrum: labeling studies with nuclear isotopes Spectra of hydrogenase (A) growth was performed with natural Ni (natural abundance of 61 Ni is 1.19%); (B) growth in the presence of 61 Ni (I = 3/2)

18 Type Identification - Nickel The Microwave Frequency A B C D Methyl-coenzyme-M reductase from Methanothermobacter marburgensis (C) natural Ni (D) growth in the presence of 61 Ni (86 %) An increase in the strength of the magnetic field B 0 will result in a larger separation of the two energy levels. As a result there will be an increased population difference between the ground and excited state resulting in higher signal amplitude. To be able to meet the resonance conditions the frequency will also have to be increased according to ν (MHz) g = B (Gauss) Cobalt The Microwave Frequency A B Co +, d 7, I = 7/2 g>g e Methyltransferase from M. marburgensis. (A) Protein as isolated. (B) Computer simulation. g xyz = , , Starting at 133 MHz just like NMR spectroscopy researchers have been pushing to get better resolution and better sensitivity. For both technical and fundamental reasons it turned out that the optimum sensitivity in EPR is reached in the 8-12 GHz range and X-band is right there in the middle of that range. There are cases, however, that the information obtained at X-band frequencies is limited and a higher frequency is needed

19 The Microwave Frequency The Microwave Frequency EPR absorption lines can have a width that is independent of the used frequency and the corresponding resonance field. As a consequence, the resolution of two partially overlapping lines will increase with increasing frequency. Note that there is a theoretical limit of maximal resolution enhancement by frequency increase. In practical cases the enhancement is usually less or in some cases there is no enhancement at all. 73 Comparison of a Vitamin B 12 spectrum at X-band (9.5 GHz) and Q-band (35 GHz). In this example, the superhyperfine lines are still resolved at Q-band, but are not overlapping with the g x - and g y -peaks anymore. Now the 8 hyperfine lines can be detected without any problems X-band Field (mt) Q-band 75 The Microwave Frequency The Microwave Frequency The Zeeman interaction is field dependent The linewidth is generally not field dependent (with the exception of g-strain). The (super) hyperfine interactions are also independent of the magnetic field. Therefore, changing the microwave frequency means changing the relative weight of the B-dependent and B- independent interactions and so the shape (and information content) of the spectrum changes with frequency. Note that by doing this, for example, the description of the high-spin systems is no longer valid. Comparison of the MCRred1 spectrum at X-band (9.5 GHz) and W-band (90 GHz). Note that the linewidth does not change on a linear Gaussscale (both scales cover 3000 Gauss). X-band W-band

20 The Microwave Frequency Identification of Ligands When the spectra are both plotted on the same g-scale is seems like the linewidth is much smaller, and small differences in g-values can be detected. In this example, the superhyperfine lines are not resolved at W-band. X-band W-band 77 Free electron in d x 2 -y 2 orbital Free electron in d z 2 orbital 79 Cobalt A Co +, d 7, I = 7/2 g>g e Methyltransferase from M. marburgensis. (A) Protein as isolated. (B) Computer simulation Vanadium V 4+ d 1 I = 7/2 B g xyz = , , The position of the 8 hyperfine lines are indicated in the figure. Each line, in turn, is split due to interaction with a N-ligand Vanadium-containing chloroperoxidase from the fungus Curvularia inaqualis

21 Vanadium Tungsten Spectrum is due to V 4+ d 1, I = 7/2 A W 5+, d 1 Formyl-methanofuran dehydrogenase (FDH II) from cells grown on tungstate. The spectrum is axial: g // = 1.95 and g = 1.98 (g<g e ) Both lines are split into 8 hyperfine lines. The hyperfine splitting A is very large and the hyperfine lines of one peak will be on the other side of the other peak. This causes an effect called overshoot: The orientation and shape of these lines will change. B (A) g xyz = , , (B) Simulation of C based on the natural abundance of the tungsten isotopes: I = 0: 180 W, 0.14%; 182 W, 26.4%; 184 W, 28.4% and I = 1/2: 183 W, 14.4% Molybdenum Copper A B Mo 5+, d 1 Methanobacterium wolfei formylmethanofuran dehydrogenase (FDH I) isolated from cells grown on molybdate Cu 2+ in Cu(ClO 4 ) 2 d 9, I = 3/2 Axial signal (g>g e ) (A) Two signals with g xyz = 2.003, 1.989, and g xyz = 2.00, 1.984, (B) Cells grown in the presence of 97 Mo-molybdate (I = 5/2). Note that we have g-values above and below g e

22 Copper S=1/2 Systems B 0 ΔE Absorption Comparison of EPR spectra and structures for copper centres in azurin. a, Type 1 (wildtype). b, Type 0 (C112D/M121L). c, Type 2 (C112D). (Rosenzweig (2009) Nature Chemistry, 1, ) 85 st 1 Derivative Resonance condition: E = hν = g e βb 0 87 Iron-sulfur Clusters [2Fe-2S] 1+ S = ½ [2Fe-2S] 2+ S = 0 [3Fe-4S] 0 S = 2 [3Fe-4S] 1+ S = ½ [4Fe-4S] 1+ S = ½ [4Fe-4S] 2+ S = 0 (HiPIP) [4Fe-4S] 2+ S = 0 [4Fe-4S] 3+ S = ½ K 4-10 K 4-20 K 4-10 K 86 High-Spin Systems A system with n unpaired electrons has a spin equal to S = n/2. Such a system has a spin multiplicity: m s = 2S + 1 This value is equal to the number of spin energy levels. All the spin levels together are called the spin multiplet. An essential difference between S = ½ systems and high-spin or S 1 systems is that the latter are subject to an extra magnetic interaction namely between the individual unpaired electrons. Unlike the electronic Zeeman interaction this interaction is always present and is independent of any external field. Another name for this interaction therefore is zerofield interaction

23 (non-)kramers Systems Systems with more than one unpaired electron Half-integer / Kramers systems S = 3/2, 5/2, 7/2, 9/2 All systems detectable in perpendicular-mode EPR Integer / non-kramers systems S = 1, 2, 3, 4 Detection in parallel-mode EPR In biochemistry only relevant for S = 2 systems of [3Fe-4S] 0 and Heme-Fe 2+ The Ni 2+ in MCR is S =1 but does not display a spectrum 89 Half-Integer / Kramers systems The spin Hamiltonian becomes H s = βb g S + S D S Solving the wave equations it can be shown that in zero field, the sub levels of a half-integer spin multiplet group in pairs (Kramer pairs) and these pairs are separated by energy spacings significantly greater than the X-band microwave energy hν. These spacing are also called zero-field splittings, or ZFS. 91 Examples for Fe 3+ /S = 5/2 Energy Levels for S = 5/2 System Example 1: Fe 3+ in rubredoxins. The ion is coordinated by the thiolate groups of four Cys residues. Rubredoxin (Photosystem II) m S = ±5/2> m S = ±3/2> Example 2: Fe 3+ in the heme group of KatG. The ion is coordinated by the four nitrogen ligands from the heme ring. KatG m S = ±1/2> The S = 5/2 multiplet forms three Kramers doublets that are separated from the others by energies significantly larger than the 0.3-cm -1 microwave quantum (X-band)

24 Energy Levels for S = 5/2 System Half-Integer / Kramers Systems m S = ±5/2> hν = g eff βb m S = ±3/2> m S = ±1/2> g eff encompasses the real g-values plus the effect of the zero-field interaction. Just like the g-value and A-values also the zero-field interaction parameter can be anisotropic and have three values D x, D y, and D z. The degeneracy between the pairs is lifted in an external field. Since the zero field splitting is very large, the external fieldinduced splitting only allows for the occurrence of EPR transitions within each (split) pair of levels. Only intra-doublet transitions observed in EPR Energy Levels for S = 5/2 System Half-Integer / Kramers Systems m S = ±5/2> hν = g eff βb m S = ±3/2> m S = ±1/2> There is no crossing over and mixing of the energy levels. For Kramers systems each Kramer pair can give rise to its own resonance. Each of these can be described in terms of an effective S = ½ spectrum with three effective g-values. 94 In contrast to g and A, however, the three D i s are not independent because D x 2 + D y 2 + D z 2 = 0, and so they can be reduced to two independent parameters by redefinition: D = 3D z 2 and E = D x D y 2 We can also define a rhombicity η = E D with 0 η

25 Half-Integer / Kramers Systems From the complete energy matrix it can be derived that under the so-called weak-field limit (Zeeman interaction << zero-field interaction) the three elements of the real g-tensor, g x, g y, and g z, can be fixed at 2.00 and that the shape of the EPR spectra, the effective g-values, is a function of the rhombicity E/D. The relationship of the effective g-values versus the rhombicity can be plotted in two-dimensional graphs, socalled rhombograms. Rhombogram & Simulations spectrum simulation Axial component(s) E/D = 0.00 Rhombic component E/D = K m S = ±5/2> m S = ±3/2> m S = ±1/2> Rhombogram Mn 2+ S = 1/2 E/D = S = 3/2 4.5 K m S = ±5/2> m S = ±3/2> m S = ±1/2> The somewhat simplified description of the EPR spectra of the different Fe 3+ systems and iron-sulfur-cluster containing proteins was possible due to the fact that they all fall within the weak-field limit (Zeeman interaction << zero-field interaction). It is also possible that the zero-field interaction is much weaker than the Zeeman interaction, and this strongfield limit hold for six-coordinate Mn 2+, which is not only biologically relevant as a site in some manganese proteins, but also because this is a very common contaminant of biological preparations

26 Mn 2+ Mn 2+ The electronic spin state of Mn 2+ is S = 5/2. Six energy states with the electron spin magnetic quantum number, m s = 5/2, 3/2, 1/2. -1/2, -3/2, and -5/2 arise due to the Zeeman effect. 101 Due to the nuclear spin magnetic quantum number, all lines will be further split into six hyperfine lines, m = 5/2, 3/2, 1/2. -1/2, -3/2, and -5/2. Note that due to second-order effects the energy level splitting by the Zeeman effect is not linear. 103 Mn 2+ Mn 2+ Pure cubic (e.g., octahedral) situation: D and E are zero, g is isotropic, because of the high spin a new zero-field energy term exists that produces EPR anisotropy. The zero-field splitting for Bǁz are shown. 102 The energy level diagram predicts that the spectrum is dominated by the m s = +1/2-1/2 transition and shows the presence of six hyperfine lines each split by a small anisotropy induced by the zero-field splitting. Mn 2+ d 7 I = 5/2 (S = 5/2) In between the six hyperfine lines there are five pairs of weak lines from forbidden Δm I = ± 1 transitions with an order of magnitude lower intensity than the main lines. This whole ms = ±1/2 spectrum is on top of a very broad, rather structureless feature that is the sum of all the other five Δm s =1 transitions (e.g., m s = -3/2-5/2)

27 Integer / non-kramers Systems Non-Kramers systems or integer systems are systems with S = 1, 2, 3, 4. These systems are very seldom observed in biological systems. One of the reasons is that just as in the Kramers systems the energy levels are organized in doublets (and one singlet, 0 ). These doublets, however, are split even at zero field and this splitting is generally greater than the energy of the X-band radiation. This means that in most cases the signals cannot be detected. 105 S = 2 System For E 0, the signals become more rhombic and mixing of the wave function takes place Signal can be detected in perpendicular-mode EPR: Δm s = 1 or in parallel-mode EPR Δm s = 0 Since the levels are already split at B 0 = 0 the peaks will be shifted to higher g-values. 107 S = 2 System S = 2 System For E = 0, the effective g-values are g xyz = 0, 0, 4 (for ±1 doublet) and g xyz = 0, 0, 8 (for ±2 doublet), purely axial. This means that the signals are not detectable 106 Due to several mechanisms the EPR signals are very broad and deformed and not much information can be obtained from the signals itself. For most systems however this zero-filed splitting is larger than the microwave energy at X-band and no signal will be detected

28 S = 2 System Example of the spectra detected for the S = 2 [3Fe-4S] 0 cluster from hydrogenase from Allochromatium vinosum. 109 Spin-Spin Interaction In principle one could expect to see two signals for each paramagnetic species present and both signal would be split due to the spin-spin interaction. The distance of the split peaks would be dependent on the distance between the two species in the molecule This would only happen when the g-tensors of both species are linear. When the g-tensors are not parallel, however, the spectra will change significantly. 111 Hyperfine Interactions Hyperfine interaction Interaction of the electron spin with the nuclear spin of the metal ion nucleus Super hyperfine interaction Interaction of the electron spin with first coordinate sphere ligands nuclei Spin-spin interaction Interaction of the electron spin with other electron spins within 10 Å distance. Spin-Spin Interaction A) [4Fe-4S] + signal detected in a ferredoxin from Bacillus stearothermophilus. B) Signal detected in a socalled 8Fe ferredoxin from Clostridium pasteurianum. In this sample two [4Fe-4S] + clusters are present. Spectrum B does not look like two overlapping signals. A more complex signal is now detected. The broad wings in the EPR spectrum (indicated by the arrows) are typically found for two interacting clusters

29 Spin-Spin Interaction Spin-Spin Interaction Adenosylcobalamin (coenzyme B 12 )-dependent isomerases. Catalyze skeletal rearrangements via a radical mechanism. The reaction starts with the generation of the 5 - deoxyadenosyl radical and cob(ii)alamin from enzymebound adenosylcobalamin by homolysis of the coenzyme s cobalt-carbon σ-bond in the presence of a substrate molecule SH. 113 A) EPR spectrum of the Co 2+ species by itself (g av 2.18) B) EPR of the radical species by itself (g = ) C-E) The actual observed EPR spectra for different types of isomerases. 115 Spin-Spin Interaction Spin-Spin Interaction Different types of interactions dependent on the distance between the two interacting paramagnets. Stereospecific hydrogen abstraction from the substrate molecule by the 5 -deoxyadenosyl radical gives 5 - deoxyadenosine and a substrate radical S. At this point two paramagnetic species are present in the enzyme, the Co 2+ species and the S radical species. 114 Through-space dipole-dipole interaction: anisotropic interaction that follows a 1/r 3 dependence on the spacing between the interacting centers Exchange interaction that depends on orbital overlap and spin polarization effects: isotropic interaction, which falls off approximately exponentially with the distance between the partners

30 Weakly Coupled Spin Systems Strongly Coupled Spin Systems At distances greater than approximately 9 Å, the exchange interaction creates a doublet splitting in the EPR spectrum of each partner At closer distances, the exchange interaction mixes the two spin systems, such that their g-values become averaged and eventually converge to a triplet state at interspin separations of <7 Å. At distances greater than approximately 9 Å, the exchange interaction creates a doublet splitting in the EPR spectrum of each partner At closer distances, the exchange interaction mixes the two spin systems, such that their g-values become averaged and eventually converge to a triplet state at interspin separations of <7 Å Weakly Coupled Spin Systems Strongly Coupled Spin Systems EPR spectrum of hydroxyethylhydrazineinactivated ethanolamine ammonia-lyase showing the presence of features corresponding to B 12r and a companion radical species with absorption near g = 2.0. The signals from the low-spin Co 2+ and the partner radical were split by a combination of exchange and dipole-dipole coupling. This can be detected as the additional hyperfine splitting of the Co 2+ signal. The amplitude of the signal of the radical centered at g = 2.0 is off scale. 118 Simulation of signals: For distances larger than 4-5 Å both paramagnets can be considered point dipoles. The zero-field splitting is described as a traceless tensor with an axial, D, and a rhombic, E, term. In the commonly used point-dipole approximation, E 0. The principal axis of the zero-field splitting normally contains the interspin vector. In simulations, Euler rotations (θ) are required to relate the axis system of the zero-field splitting tensor to a reference system, such as the g-axis of Co

31 Strongly Coupled Spin Systems Very Strongly Coupled Spin Systems When there is a strong coupling between the cobalt and the radical species, the EPR spectra becomes a hybrid of both the cobalt and the radical EPR signals and exhibit an average g-value of 2.1 that arises from coupling between a carbon centered radical (g = ) with cob(ii)alamin (g av 2.18). The signals are due to a hybrid triplet spin system comprising both paramagnets. 121 When there is a very strong coupling the EPR spectrum does not resemble that of Co 2+ or a radical species. However, it is still consistent with a rhombic triplet-state species. A prominent half-field transition at around g = 4 can be detected (not shown). Note that the EPR spectrum covers a wide area. The close spacing of the unpaired electrons, together with the spin delocalization within the allylic radical, requires a higher level of treatment than the point-dipole approximation. 123 Strongly Coupled Spin Systems (C) Signal of the coupled Co 2+ /radical species in ethanolamine ammonia lyase after reacting with ethanolamine. The interspin distance is 8.7 Å and θ = 25 (D) Coupled Co 2+ /radical species in lysine-5,6- aminomutase after reacting with 4-thialysine. The interspin distance is 7.0 Å and θ = Very Strongly Coupled Spin Systems (E) Coupled Co 2+ /radical species in diol dehydratase after reacting with 5 -deoxy-3,4 - anhydroadenosylcobalamin. The interspin distance is 3.5 Å and θ =

32 g-strain We know from folding studies and from structural NMR and X-ray studies that samples of proteins come with a distribution of conformations. For EPR this means that the paramagnet in each molecule has a slightly different structural surrounding and thus a slightly different g-value. This structural inhomogeneity or g-strain is reflected in the spectroscopy in the form of an inhomogeneous line shape. This normally results in a change from a Lorentzian to Gaussian line shape. An important consequence of this g-value anisotropy is that the line width, W, is in general, also isotropic. 125 g-strain The most noticeable difference is now that the linewidth, plotted on a g-scale does not change when the spectra are measured at higher frequency. This effect is shown in the figure for the [4Fe-4S] cluster detected in spinach-leaf ferredoxin. The line width is very similar in the range of 35 to 3.3 GHz. At 1.1 GHz a broadening is detected due to unresolved hyperfine coupling. 127 g-strain Most of the time we do not have to worry about this, but particularly in the EPR spectra of the iron-sulfur clusters g-strain can have a big effect on the shape of the EPR spectrum and therefore on the simulation and interpretation of the EPR data. 126 ENDOR Nuclear hyperfine splitting might not always be resolved but might be hidden in the EPR peaks. Techniques have been developed to detect these interactions: Electron-Nuclear Double Resonance (ENDOR), Electron Spin Echo Envelope Modulation (ESEEM), and HYperfine Sublevel CORrElation (HYSCORE) spectroscopies. In transition metal complexes and metalloproteins, magnetic nuclei such as 1 H, 2 H, 13 C, 14 N, 15 N, 17 O, 31 P and 33 S, in the vicinity (2-12 Å) of the paramagnetic metal ion can be detected by these techniques. Identification of the presence of a particular ligand nucleus, and under favorable circumstances metalligand nuclei distances and angles can be obtained

33 ENDOR Energy level diagram for an S = ½, I = ½ spin system. The g-value and hyperfine coupling are assumed to be isotropic. The red lines show the allowed EPR transitions and the stick EPR spectrum. The blue lines show the NMR (ENDOR) transitions and the stick ENDOR spectrum. 129 ENDOR Using higher MW power, the E 1 E 3 transition becomes saturated such that the spin population in both levels equalizes (b), a situation that should be avoided in regular CW EPR spectroscopy since the signal intensity will decrease to almost zero. To restore the EPR signal intensity, a population difference between the levels E 1 and E 3 needs to be created. 131 ENDOR ENDOR The energy levels for an S = ½, I = ½ spin system Using low MW powers, resonance absorption occurs as, for example, the EPR II transition frequency E 1 E 3 is induced but rapid relaxation ensures that the excited spins return quickly to the ground state leading to an unsaturated EPR signal (a). 130 Two mechanisms: One way is by pumping the RF transition E 3 E 4 (NMR I) using a saturating RF field (c). An enhancement of the EPR absorption is detected if the irradiated RF frequency is resonant with this transition. This enhancement represents the first ENDOR signal

34 ENDOR ENDOR In an alternative way, the RF transition E 1 E 2 (NMR II) can be pumped (Fig. 39d). This also creates an enhancement and represents the second ENDOR resonance line. 133 C) 31 P-ENDOR spectra. Spectra were collected at the fields and g-values indicated, and are shown alongside the respective pulse-echo detected EPR spectra. A cluster- 31 P distance of 6.6 Å was calculated 135 ENDOR Pulsed ENDOR A) EPR spectrum obtained for IspG upon incubation with the substrate MEcPP and the reductant dithionite B) Proposed structure for the reaction intermediate 134 The Davies ENDOR sequence (π MW -π RF -π/2 MW -τ-π MW -τecho) is the pulsed equivalent of a CW ENDOR experiment. The effect of this sequence on the occupation of the energy levels for the two-spin system (S = ½, I = ½) is shown

35 Pulsed ENDOR ESEEM The first selective π MW pulse inverts the electron spin populations in the E 1 and E 3 manifolds (a) inducing the transition EPR II. This is followed by a π RF pulse that inverts the nuclear spin populations upon resonance with an NMR transition (NMR I, b). 137 Electron Spin Echo Envelope Modulation (ESEEM) is an important technique for measuring the hyperfine interaction parameters between electron spins and nearby nuclear spins. From the analysis of the ESEEM signals detailed information about electron spin density distribution, distances and bonding angles is gained. 139 Pulsed ENDOR ESEEM The remaining sequence consists of either the selective (c) or non-selective (d) electron-spin echo detection pulses. 138 With ESEEM the NMR frequencies are observed indirectly through observation of the mixing of allowed and (formally) forbidden EPR transitions as modulations superimposed on a time-decaying spin-echo. Echo envelope modulation occurs when state mixing of hyperfine levels occurs. Fourier transformation of the modulated time trace results in spectra in the frequency domain containing the nuclear frequencies

36 2D-HYSCORE 2D-HYSCORE An extension of ESEEM is HYperfine Sub-level CORrElation (2D-HYSCORE). This technique is essentially a two dimensional ESEEM experiment in which correlation is transferred from one electron spin manifold to another. HYSCORE allows one to take a complicated ESEEM spectrum and extend the data into a second dimension. The nuclear coherence generated by the first two π/2 pulses undergoes free evolution during time t 1 with frequency ω 12 (ω 34 ). The mixing π pulse then transfers populations in one m s manifold to the other and similarly transfers the nuclear coherence between manifolds so that it evolves with frequency ω 34 (ω 12 ) during time t 2. The modulated time decay data is subsequently Fourier transformed in both dimensions (i.e. t 1 and t 2 ) to produce a 2D frequency-domain spectrum (with axes ν 1 and ν 2 ) D-HYSCORE 2D-HYSCORE The HYSCORE pulse sequence is a four-pulse MW sequence in which an additional mixing π pulse is inserted between the second and third π/2 pulse of the three-pulse ESEEM Experiment. The two inter-pulse delays, t 1 and t 2, are varied independently to produce a two-dimensional (2D) time delay array. The nuclear frequencies from the different m s manifolds are correlated and appear as cross-peaks at the frequencies (ν 1, ν 2 ), (ν 2, ν 1 ), and (ν 1, -ν 2 ), (ν 2, -ν 1 ) in the (+,+) and (+,-) quadrants of the 2D spectrum, respectively. As strong cross peaks can only be observed between NMR frequencies of the same nucleus, HYSCORE spectra can be significantly simplified compared to threepulse ESEEM

37 2D-HYSCORE 2D-HYSCORE Another advantage of HYSCORE spectroscopy is that the frequencies from weakly-coupled nuclei ( a iso < 2 ν L ) appear as cross-peaks in the (+, +) quadrant, whereas strongly-coupled nuclei ( a iso > 2 ν L ) are observed in the (+, ) quadrant (a). This facilitates spectral interpretation for systems containing many interacting nuclei such as metalloenzymes or proteins C and 17 O HYSCORE Spectra of the FeS A species in IspG 147 2D-HYSCORE Summary +½: E = +½g e βb 0 -½: E = -½g e βb 0 For disordered systems with broad ESEEM features, the correlation peaks broaden into ridges, as illustrated for the two-spin system (S = ½, I = ½) with an axial hyperfine tensor (b). The anisotropy of the dipolar hyperfine interaction, T, can be determined from the maximum curvature of the ridges away from the antidiagonal, labelled ω max, and the magnitude of a iso can be found from the ridge end points or from simulation. 146 Resonance condition: E = hν = g e βb 0 For X-band: g = ν (MHz) B (Gauss)

38 Quantum Mechanical Description Simplified Schrödinger wave equation H s ψ s = Eψ s H s = βb g S + S A I + S D S + Zeeman interaction Hyperfine interaction Zero field splitting or spin-spin interaction Can sometimes be solved under a set of assumptions Solutions sometimes analytical, sometimes need for numerical approach Cannot allows be solved 149 Line Shape of EPR Spectra for High-Spin Systems Half-integer/non-Kramers: S = 3/2, 5/2, 7/2, 9/2 Rhombograms will help with the identification of the spin state, determination of which spin doublets are detectable and determination of the E/D value. 151 Line Shape of EPR Spectra for S = ½ Systems Four basic shapes. Examples for Fe 3+ /S = 5/2 m S = ±5/2> When more than three peaks are detected the signal could be split due to spin interaction or there could be more than one signal present. Rubredoxin (Photosystem II) KatG m S = ±3/2> m S = ±1/2>

39 Practical Aspects of EPR Spectrometry 1) Metal-Ion Type Identification 2) Optimal Measuring Conditions (T,P) 3) The X-band EPR Spectrometer 4) Spectrometer Parameters 5) Spin Intensity 6) Redox Titrations 7) Freeze-Quench Experiments 8) Simulation of EPR Spectra 9) EPR on Whole Cells/Cell Extract 10) Site-Directed Spin Labeling (SDSL) EPR 153 Metal-Ion Type Identification Has the metal a nuclear spin? Atom Isotope Spin (abundance) V 50, V, 6 (0.25); 51 V, 2 (99.75) Mn Fe 54, 56, 57, (2.119) Co Ni 58, 60, 61, (1.14) Cu 63, Cu, 2 (69.17); 65 Cu, 2 (30.83) Mo 92, 94, 95, 96, 97, 98, Mo, 2 (15.92); 97 Mo, 2 (9.55) W 180, 182, 183, 184, (14.3) Is the signal going to be split into 2 I + 1 lines? In general: The spin orbit coupling parameter is positive for systems with less than half filled outer shells and negative for those with more than half filled shells, which means that the former have g<g e and the latter have g>g e ) Metal-Ion Type Identification Which redox state is EPR active? Metal Ion Electron Configuration Spin State Fe 2+ d 6 S = 0 (ls) or S = 2 (hs) Fe 3+ d 5 S = 5/2 (hs) Ni 1+ d 9 S = ½ Ni 2+ d 8 S = 0 or S = 1 Ni 3+ d 7 S = ½ Cu 1+ d 10 S = 0 Cu 2+ d 9 S = ½ Prepare different samples: 1) as such 2) reduced (dithionite) 3) oxidized (ferricyanide) How many unpaired electrons? Different spin states! 154 2) Optimal measuring Conditions (T, P) There is a need to measure at lower temperatures! EPR frequencies (1-100 GHz) are in the microwave range! Aqueous solutions will warm up in the EPR cavity at RT! This effect is absent in frozen samples. Do-it-yourself microwave source

40 The Need for Lower Temperatures The energy difference between the two energy level due to the Zeeman splitting is very small, ~0.3 cm -1 for X-band EPR. Based on the Boltzmann distribution n 1 = n 0 e E kt it can be shown that only at low temperatures there will be enough difference in the population of the S = -½ level (n 0 ) and the S = ½ level (n 1 ) to create a signal. 157 Heisenberg Uncertainty Principle Due to the uncertainty principle the EPR spectra will broaden beyond detection at higher temperatures. At lower temperatures the spectra will sharpen up. This sharpening up of the spectrum by cooling the sample is, however, limited by a temperatureindependent process: inhomogeneous broadening. The protein or model molecules in dilute frozen solutions are subject to a statistical distribution in conformations, each with slightly different 3D structures and, therefore, slightly different g-values, which manifest themselves as a constant broadening of the EPR line independent of the temperature. 159 Spin-Lattice Relaxation What to Do? POWER SATURATION OPTIMAL CONDITIONS TEMPERATURE BROADENING EPR on metalloproteins: the relaxation rate decreases with decreasing temperature; and the relaxation rate is anisotropic (i.e. is different for different parts of the spectrum). When too much power is applied the signal will saturate: Power saturation! 158 Optimal measuring conditions (T,P) are determined by the interplay of the Boltzmann distribution, the Heisenberg uncertainty relation, the spin lattice relaxation rate, and the conformational distribution of molecular structure. How do I find the correct measuring condition? 1) Make a Curie Plot 2) Make Power Plots

41 Power Plots Power Plot (Copper Perchlorate) The power in EPR is expressed in decibels (db) attenuation X-band microwave sources have a constant output that is usually leveled off at 200 mw (= 0 db): P(dB) = 10 log(0.2/p(w)) logarithmic scale: every -10 db attenuation means an order-of-magnitude reduction in power. A good X-band bridge operates at power levels between 0 and -60 db Power Plots Relationship between the amplitude, gain and the power in db: amplitude 10 db 20 = constant gain Both power and gain scales are logarithmic! Need for low temperatures and high power, but this could lead to power saturation! Practical rule: the amplitude of a non-saturated EPR signal does not change if a reduction in power by -1 db is compensated by an increase in gain by one step. 162 Power Plot (Copper Perchlorate) The relaxation rate increases with increasing temperature. Therefore if a signal does not saturate at a certain power at a certain temperature it will also not saturate at the same power at a higher temperature. The temperature behavior or Curie behavior will be different for different species

42 Curie Plot (Copper Perchlorate) Line Shape I n = I db 0 T gain I n, normalized value for the intensity; I 0, observed intensity; T, absolute temperature in K; db, reading of the attenuator; gain, gain 165 The basic form of an EPR peak is described by the Lorentz distribution. The Lorentzian line shape is also frequently called the homogeneous line shape. In biological samples the paramagnet in each molecule has a slightly different structural surrounding and thus a slightly different g-value. This structural inhomogeneity is reflected in the form of an inhomogeneous line shape in addition to the Lorentzian shape. At low temperature the contribution from homogeneous broadening is small and the line shape can be described by the Gaussian distribution. 167 Curie Plot Line Shape 166 At relatively high temperature a Lorentzian line shape will be observed, while a Gaussian line will be observed at relatively low temperatures The Gaussian shape will be broader. Preference to measure at the higher temperature end of Curie plot Practice better signal-tonoise at the lower end

43 Power Plots Note that there are different ways to compose power plots. Plot A shows the signal intensity vs. power (-db) with no correction. Plot B show the signal intensity versus P (in mw). In this case there is a linear relationship as long as the sample does not saturate (indicated by the straight line). Plot C uses the earlier described method on slide EPR Spectrometer Varian E3 Bruker ElexSys X-band Varian E4 Bruker ElexSys W-band 171 3) The X-band EPR Spectrometer In 1944, E.K. Zavoisky discovered magnetic resonance. Actually it was EPR on CuCl 2. X-Band EPR Spectrometer E.K. Zavoisky s first EPR system

44 X-Band EPR Spectrometer Microwave bridge 173 The produced radiation is transferred by means of a rectangular, hollow wave guide to an attenuator where the 200 mw can be reduced by a factor between 1 and On the left is a monochromatic source of microwaves of constant output (200 mw) and slightly (10%) tunable frequency. 174 The output of the attenuator is transferred with a waveguide to a circulator that forces the wave into the resonator/cavity. The entrance of the resonator is marked by the iris, a device to tune the amount of radiation reflected back out of the resonator

45 The reflected radiation returns to the circulator and is directed to the diode for the detection of microwave intensity. 177 A small amount of the 200 mw source output is directed through the reference arm directly to the detector to produce a constant working current. The reference arm contains a port that can be closed and a device to shift the phase of the wave. 179 X-Band EPR Spectrometer Any remaining radiation that reflects back from the detector is forced by the circulator into the upward waveguide that ends in a wedge to convert the radiation into heat. 178 Most EPR spectrometers are reflection spectrometers. They measure the changes (due to spectroscopic transitions) in the amount of radiation reflected back from the microwave cavity containing the sample. The detector should only detect the microwave radiation coming back from the cavity

46 Cavity/EPR Resonator Cavity/EPR Resonator A microwave cavity is simply a metal box with a rectangular or cylindrical shape which resonates with microwaves much as an organ pipe resonates with sound waves. The resonator is designed to set up a pattern of standing microwaves in its interior. Standing electromagnetic waves have their electric and magnetic field components exactly out of phase - where the magnetic field is maximum, the electric field is minimum. 181 Cavities are characterized by their Q or quality factor, which indicates how efficiently the cavity stores microwave energy. We can measure Q factors easily: Q = (ν res )/(Δν) where ν res is the resonant frequency of the cavity and Δν is the width at half height of the resonance. 183 Cavity/EPR Resonator Cavity/EPR Resonator Resonance means that the cavity stores the microwave energy; therefore, at the resonance frequency of the cavity, no microwaves will be reflected back, but will remain inside the cavity. Energy can be lost to the side walls of the cavity because the microwaves generate electrical currents in the side walls of the cavity which in turn generates heat. 182 In order for the microwaves to enter the cavity one of its end walls must have an opening: iris. The size of the iris controls the amount of microwaves which will be reflected back from the cavity and how much will enter the cavity. Just before the iris is a small metal plate (attached to the iris screw). Moving this plate up or down changes the amount of coupling. Only for one unique position is the cavity critically coupled: all waves enter the cavity, and no radiation is reflected out

47 Cavity/EPR Resonator How do all of these properties of a cavity give rise to an EPR signal? When the sample absorbs the microwave energy, the Q is lowered because of the increased losses and the coupling changes. The cavity is therefore no longer critically coupled and microwaves will be reflected back to the bridge, resulting in an EPR signal. 185 Tuning the Microwave Cavity and Bridge Locate and center the dip on the display. The pattern is a display of the microwave power reflected from the cavity and the reference arm power as a function of the microwave frequency. The dip corresponds to the microwave power absorbed by the cavity and thus is not reflected back to the detector diode. By centering the dip on the display monitor, the microwave source is set to oscillate at the same frequency as the cavity resonant frequency 187 Tuning the Microwave Cavity and Bridge Tune the signal (reference) phase. Adjust the Signal Phase until the depth of the dip is maximized and looks somewhat symmetric. Adjust the bias level. Adjust the Bias until the Diode meter needle is centered. 186 Critical coupling of the cavity. Power is increased and the iris screw is adjusted to keep the diode current in the center

48 4) Spectrometer Parameters Center Field and Sweep Width Spectrum Settings Gain For initial broad scans, a Sweep Width around 5000 Gauss is recommended. Set the Center Field value to 2600 Gauss. This means that the scan will start at 100 Gauss and stops at 5100 Gauss (2500 Gauss below and 2500 Gauss above the Center Field value). This scan will cover the complete area available with our magnet where signals might be detectable. 189 Use the full range of the digitizer (a), coincides with the screen display. If the receiver gain is too low the effect of digitization will be evident in the spectrum (b) At too high gain the signals will be clipped due to an overload in the signal channel (c). 191 Spectrum Settings Microwave Bridge Parameters Points Standard 1024 points. Can be increased to 4096 for wide scans to keep the resolution. It is advisable, however, to rescan the interesting parts of a wide scan. Microwave power level. The EPR signal intensity grows as the square root of the microwave power in the absence of saturation effects. When saturation sets in, the signals broaden and become weaker. Several microwave power levels should be tried to find the optimal microwave power. Subtractions are not possible if the amounts of points between the two spectra are different

49 Phase Sensitive Detection Enhancement of the sensitivity of the spectrometer: less noise from the detection diode and the elimination of baseline instabilities due to the drift in DC electronics. The magnetic field at the site of the sample is modulated (varied) sinusoidally at the modulation frequency. If there is an EPR signal, the field modulation quickly sweeps through part of the signal and the microwaves reflected from the cavity are amplitude modulated at the same frequency. Only the amplitude modulated signals are detected. Any signals which do not fulfill these requirements (i.e, noise and electrical interference) are suppressed. 193 Field Modulation With more magnetic field modulation, the intensity of the detected EPR signals increases; however, if the modulation amplitude is too large (larger than the linewidths of the EPR signal), the detected EPR signal broadens and becomes distorted. A good compromise between signal intensity and signal distortion occurs when the amplitude of the magnetic field modulation is equal to the width of the EPR signal. Also, if we use a modulation amplitude greater than the splitting between two EPR signals, we can no longer resolve the two signals. 195 Phase Sensitive Detection For an EPR signal which is approximately linear over an interval as wide as the modulation amplitude, the EPR signal is transformed into a sine wave with an amplitude proportional to the slope of the signal. As a result the first derivative of the signal is measured. Signal Channel Parameters Modulation frequency: normally set to 100 khz Modulation amplitude: You can start with 6 Gauss. The larger this value the lower the value needed for the Receiver Gain, which means less noise. Excessive field modulation, however, broadens the EPR lines and does not contribute to a bigger signal. As a rule-of-thumb this value has to be smaller than the line width of your signal. Two new parameters: modulation amplitude, and frequency

50 Time Constant To further improve the sensitivity, a time constant is used to filter out more of the noise. Time constants filter out noise by slowing down the response time of the spectrometer. As the time constant is increased, the noise levels will drop. If we choose a time constant which is too long for the rate at which we scan the magnetic field, we can distort or even filter out the very signal which we are trying to extract from the noise. Also, the apparent field for resonance will shift. 197 Signal Averaging Very weak signals might get lost in the noise. You can increase your signal to noise ratio by signal averaging. The resultant signal to noise is proportional to N, where N is the number of scans. With a perfectly stable laboratory environment and spectrometer, signal averaging and acquiring a spectrum with a long scan time and a long time constant are equivalent. Unfortunately perfect stability is impossible to attain. Slow variations result in baseline drifts. For a slow scan (>15 min) the variations can cause broad features in the spectrum dependent on the sample concentration and the gain used. If you were to signal average the EPR signal with a scan time short compared to the variation time, these baseline features could be averaged out. 199 Signal Channel Parameters Time Constant and Conversion Time: If the Time Constant is too large in comparison with the Conversion Time (the rate at which the field is scanned) the signals we want to detect will get distorted or will even be filtered out. A longer Conversion Time, however, also improves the signal to noise ratio in a different way: The signal channel incorporates an integrating ADC (Analog to Digital Converter) to transfer the analog EPR spectra to the digital data acquisition system. An important side effect of using the integration method for the conversion is that it integrates the noise out of the signal. With a sweep width off about 1000 Gauss a Conversion Time of msec and a Time Constant of msec can be used. 198 Spectrometer Parameters Center Field, Sweep Width, Gain, Microwave power level: sample dependent Modulation frequency: normally set to 100 khz Modulation amplitude: normally set to 6 Gauss. Time Constant and Conversion Time: same value! sweep width off 1000 Gauss; both msec Number of X-Scans: normally set to

51 5) Spin Intensity Also known as spin counting To calculate the amount of signal in a protein sample, the spin intensity can be compared with that of a standard with a known concentration (Copper perchlorate: 10 mm) Since an EPR spectrum is a first derivative, we have to integrate twice to obtain the intensity (I 0 = area under the absorption spectrum). In addition, corrections are needed for a number of parameters, to normalize the spectra. Only then a direct comparison of double integral values of standard and unknown is possible: Signal Integration Step 1: select spectrum Normalized Signal Intensity Signal Integration where I n I 0 d T db f a and I n = I 0 d 2 db T g av p f a normalized double integral observed intensity distance between the starting and ending points (in Gauss) absolute temperature in K reading of the attenuator tube calibration factor gain g p av = 2 3 g x 2 +g y 2 +g z g x +g y +g z Step 2: select area to integrate (shown is the first integral)

52 Signal Integration Signal Intensity??? Clostridium pasteurianum [2Fe-2S] 2+ S = 9/2 (D < 0) Step 3: get the value for the double integral Comparison with Spin Standard I n = I 0 d 2 db T g av p f a C u = I n(u) C st I n(st) Keep measuring conditions the same: temperature, modulation amplitude, sweep time, amount of points, amount of scans (These are not averaged!) Measure samples on the same day! Correct for spin: S(S+1) Signal Intensity??? The effective spin-hamiltonian suggests an easy way for quantification of high-spin spectra: one simply applies the double-integration procedure to the effective S eff = 1/2 spectrum as if it were a real S = 1/2 spectrum, however, with a correction for the fractional population of the relevant doublet. (Most of the time not possible!) Exception: For high spin ferric hemoproteins (D +10 cm 1 ) in X-band at T = 4.2 K the fractional population of the m S = ±1/2> doublet is very close to unity (0.999) therefore, quantification of the spectrum does not require a depopulation correction

53 Signal Intensity??? Simulations will be needed to get the signal intensity of a signal when more than one signal is present, the signal intensity is too low (too much noise), or the baseline is not linear. Spectrum Simulation Difference 209 Redox Titrations When there is only a single paramagnetic species present the intensity of this signal can be determined directly. When more than one species are present you have to look for unique features, or the different components have to be simulated and their intensities determined. Plots of the intensity vs. the potential are generated. The points in the plot can be fitted with the Nernst equation: E = E 0 + RT nf ln [ox] [red] R (gas constant) = J K 1 mol 1 ; F (Faraday constant) = C mol 1 ; n is the number of moles of electrons 211 6) Redox Titrations Redox Titrations With species that are only paramagnetic at a certain redox potential it is possible to do a redox titration and obtain the midpoint potential (E m ) of the redox couple. This is particular useful if you are studying proteins that are involved in electron transfer pathways. In these experiments the protein is titrated in both the oxidative direction with ferricyanide and in the reductive direction with dithionite. The potential can be measured with a combination Ag/AgCl electrode, A mixture of redox dyes is added to stabilize the redox potential outside the E m region 210 Heterodisulfide Reductase/Hydrogenase Complex: Found in the cytosol of some Methanogens Electrons from hydrogen are used to break down the heterodisulfide CoB-S-S-CoM which allows the reuse of both cofactors. A proton gradient is generated in this process Except for one, all clusters are involved in electron transport

54 Redox Titrations One unique cluster can either bind CoM or CoB Labeling studies with H 33 S-CoM ( 33 S: I = 3/2) 213 7) Freeze-Quench Experiments To follow a reaction involving paramagnetic species freezequench experiments can be performed. In this experiment enzyme is mixed with substrate and other compounds and EPR samples are made by rapid mixing and freezing. Multiple samples have to be made to get insight into the formation/disappearance of an EPR signal. 215 Redox Titrations Role of IspG in Isoprene Synthesis Cluster with bound HS-CoM behaves like a [4Fe-4S] 2+/3+ cluster (paramagnetic when oxidized) E m = -60 mv, ph 7.6, n =

55 Role of IspG in Isoprene Synthesis Freeze-Quench Experiments with IspG IspG contains a single [4Fe-4S] cluster. The cluster is very unstable. Cluster falls apart when exposed to molecular oxygen. Instability probably caused by incomplete coordination. Cys Cys Cys Cys 217 A transient isotropic signal is detected with maximal intensity at 90 ms. A transient rhombic signal, FeS A, reaches maximal intensity at 30 s. A second rhombic signal, FeS B, accumulates over time and reaches maximal intensity at 4 min. 219 Role of IspG in Isoprene Synthesis Freeze-Quench Experiments FeS B The reaction is a reductive elimination of a hydroxyl group involving 2 electrons. A [4Fe-4S] cluster can only donate 1 electron at-a-time. Formation of radical species expected. FeS A radical species

56 ENDOR 8) Simulation of EPR spectra There are several reason why you might want to simulate an EPR signal. For example to obtain the intensity of a particular signal in a mixture of signals. Spectrum Simulation A) EPR spectrum obtained for IspG upon incubation with the substrate MEcPP and the reductant dithionite B) Proposed structure for the reaction intermediate 221 Difference 223 2D-HYSCORE 13 C and 17 O HYSCORE Spectra of the FeS A species in IspG

57 Visual Rhombo 9) EPR on Whole Cells/Cell Extract Estimates of the effective g-values 225 CO 2 -reducing pathway of methanogenesis, which uses H 2 and CO 2 as substrates. The reduction of CO 2 to CH 4 proceeds via coenzyme-bound C1- intermediates, methanofuran (MFR), tetrahydromethanopter in (H 4 MPT), and coenzyme M (HS- CoM). CO 2 H 2 Formylmethanofuran MFR Hydrogenase Dehydrogenase CHO MFR H 4MPT MFR CHO H 4 MPT CH H 4 MPT H2 CH 2 H 4 MPT H 2 CH 3 H 4 MPT Methyl-H 4MPT:coenzyme M H 4MPT Methyltransferase CH 3 S CoM HS CoM+ HS CoB H Methyl-coenzyme M 2 Reductase Heterodisulfide CoM S S CoB Reductase CH Simulation EPR on Whole Cells Clostridium pasteurianum [2Fe-2S] 2+ S = 9/2 (D < 0) Overview of all paramagnetic species Behavior under different growth conditions Estimates of the amount of species present (simulations and integration) 5 K 20 K 70 K Field (Gauss)

58 EPR on Whole Cells The Technique A: 80% H 2 /20% CO 2 B: 80% N 2 /20% CO 2 A K Specific Cys residues are labeled with a spin label: 2,2,5,5-tetramethyl-1-oxyl-3-methyl methanethiosulfonate (MTSL). B 5 6 1) MCR (red2 form) 2) MCR (red1 form) 3) Hydrogenase (Ni-C form) 4) Heterodisulfide reductase 5) Hydrogenase (Ni-A form) 6) MCR (ox1 form) Field (mt) 229 Drawback: Cys residues have to be introduced in the structure at the positions of interest. All other accessible Cys residues need to be deleted ) Site-Directed Spin Labeling (SDSL) EPR Provides specific information on the location and environment of an individual residue within large and complex protein structures. Nitroxide Spin Labels Hyperfine Interactions: TEMPO A. Motion: Determine rotational mobility of label at different protein sites. B. Accessibility: An amino acid can be on the surface of a protein and accessible to water, or it can be placed inside the structure and is less accessible or not accessible at all. An amino acid can also be deep in the membrane space. C. Distance: Measure the distance between 2 or more amino acids in one system or between systems

59 Nitroxyl Lineshapes Freely tumbling Weakly immobilized Conventional X-band EPR spectra are sensitive to rotational motion in the range 0.1 to ~100 nsec. Nitroxyl Lineshapes g x =2.0091, g y =2.0061, g z = The field shift between the X- and Z- orientations is H=h /g x - h /g z h g/4 ~11G I=1: A x = 6.2, A y = 6.3, A z =33.6 Strongly immobilized In the fast motional limit (~0.1 nsec) three lines of approximately equal height are observed. 9.4 GHz Thomas Stockner (2105) Biochm. Soc. Trans. 43: Nitroxyl Lineshapes Freely tumbling Weakly immobilized Strongly immobilized In the motional narrowing region the three lines become broader and since the total intensity does not change the line amplitude decreases. These changes, however, vary for each of the three lines. 234 Nitroxyl Lineshapes 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 ΔB(m I ) = A + B m I + C m I 2 The dependence of the linewidth on the nuclear spin state (m I ) indicates that each line will have a different width. The A term broadens all lines equally; the C term broadens the low-and high-field lines but does not affect the center line (for which m I = 0); the B term is negative and causes the high-field (m I = -1) line to broaden and the low-field (m I = 1) line to narrow

60 Nitroxyl Lineshapes 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. Nitroxyl Lineshapes 170 GHz g x =2.0091, g y =2.0061, g z = I=1, A x = 6.2, A y = 6.3, A z =33.6 High field EPR spectroscopy is the g- resolved spectroscopy, the regions corresponding to different orientations of the magnetic axis relative to the external magnetic field do not overlap. Note that using a different frequency will change the time scale of the experiment Nitroxyl Lineshapes Freely tumbling Weakly immobilized Strongly immobilized Strongly immobilized corresponds to the slow motion limit (>100 nsec). The spectrum is very similar to the powder or rigid limit spectrum that is obtained for any nitroxide in the absence of rotational motion and for a dilute powder or frozen solution 238 A. Motion Attachment of the spin label to even a small unstructured peptide can result in some degree of motional restriction, and this restriction increases significantly in the presence of local secondary structure

61 MTSL-15 AA peptide Spin Label Mobility Based on EPR Spectra Line Shape The motion of the spin label side chain is sensitive to tertiary contacts and protein structure in the local environment of the spin label. A. dilute solution of MTSL fast motional limit (~0.1 nsec) B. attached to 15 AA peptide with random coil structure C. attached to same peptide with an α-helical structure D. No motion (slow motion limit, >100 nsec) or in frozen solution 241 (C) Mobility map constructed as a plot of the inverse second moment of the EPR spectrum (<H 2 > 1 ) versus inverse central line width (ΔH 0 1 ), which indicates the correlation between the measured parameters and regions of protein topology. 243 Spin Label Mobility Based on EPR Spectra Line Shape Mobility Map (A) motionally restricted spin label of a buried side chain of a helix and (B) increased mobility of an exposed side chain of the same helix forming β spectrin lipid-binding domain The separation between the outer hyperfine extrema (2A par ) and the peak-to-peak separation of the central line width (ΔH 0 ) provide a measure of label mobility. Czogalla, A. (200&) Acta Biochim Polonica 54:

62 B. Accessibility An amino acid can be located on a solvent-exposed surface, buried within a protein, or within a membrane bilayer. Power Saturation Studies Three common reagents: Oxygen small and hydrophobic generally found in the center of lipid bilayers of membranes and in hydrophobic pockets of proteins Only present to a small extent in solution Ni(II) ethylendiaminediacetate (NiEDDA) Neutral/Water soluble Chromium Oxalate (CROX) Negative/Water soluble Power Saturation Studies Under nonsaturating conditions, the amplitude of the spectral lines are proportional to the incident microwave power, increasing linearly with the square root of the incident power, P or P 1/2. Under saturation conditions the increase becomes less than linear. Power Saturation Studies The spin label is in a watersoluble environment. CROX and NiEDDA prevent saturation (in comparison with the N 2 curve), while O 2 does have a much smaller effect. When paramagnetic relaxation reagents interact with the spin label, they enhance the relaxation rate and allow the sample to absorb more power before becoming saturated

63 T4 lysozyme 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 α-helical structure of this segment of the protein. 249 C. Distances Measure the distance between 2 spin labels. This can be intramolecular distances between two labels in the same monomer or intermolecular distances between sites on different proteins. Binding processes, conformational changes In the range ~8-20 Å, interactions between the two paramagnets give rise to distancedependent line broadening in CW EPR. 251 Depth Parameter Distances: Pulse EPR DEER (Double Electron-Electron Resonance) is a pulse EPR technique that measures the dipolar frequency between two spins. Deer can cancel out all interactions resulting in an EPR spectrum except the dipole interaction in spin pairs. The dipolar Pake pattern shown is an FT of the DEER echo. 2 e / r [ MHz]/ 2 3 dipolar r [Å] [O 2 ] is highest in the center of the membrane and lowest at the surface. The opposite is true for the [NiEDDA]. The natural log of this ratio yields Φ, a parameter with a linear dependence on depth into the bilayer. 250 Interspin distance= 30.9Å Example: spin labeled Gramicidin A dipolar, MHz,

64 Solutions Effect of Deuterium 3) Three protons (I = ½) with A = 40 G 4) Three deuterium (I = 1) with A = 12.4 G Radicals 1) Frequency = 9500 MHz B-min = 3300 Gauss B-max = 3500 Gauss. g = 2, W = 3, A = 0 Unresolved Hyperfine Effects 5) Proton 1: A = 20 G Proton 2: A = 10 G Proton 3: A = 5 G 2) I-spin = 2/2 A-value = 25 Gauss A-value = 15 Gauss A-value = 5 Gauss A-value = 2 Gauss As. the value of A come close to the line width of the signal, the hyperfine lines start to cancel each other (A = 5, green line) or only a small broadening of the signal is detectable which is called unresolved hyperfine splitting (A = 2, purple line). The A = 0 spectrum is overlain (dash/dot) for comparison 254 Just as in exercise 2, the splitting between the lines is very close to the line width. (You can try a much smaller line width (like 1 or 0.5 Gauss) to show the complete hyperfine pattern

65 Hyperfine Patterns Ethanol Radical 6) Frequency, 9500 MHz; B-min, 3300 Gauss; B-max, 3500 Gauss. CH 3 CH OH Rh-diazo radical: Two N interactions with identical A. For nitrogen 1: A-value = 10 G For nitrogen 2: A-value = 10 G MNP-C : Interaction with 1 N (large A) and 1 H (smaller A) For nitrogen: A-value = 15 G For hydrogen: A-value = 4 G 257 7) Signal is split into four due to the three Hβ. There is an additional split into two due to the single Hα. 259 Hyperfine Patterns Hyperfine Patterns DMPO-C : Interaction with 1 H (large A) and 1 N (smaller A) For nitrogen: A-value = 30 G For hydrogen: A-value = 40 G DMPO-N : Similar interaction with 1 H (large A), 1 N (smaller A) and 1 N (even smaller A) For hydrogen: A-value = 50 G For nitrogen 1: A-value = 40 G For nitrogen 2: A-value = 10 G 258 The first multiplet (A) induces a small two-fold split due to one I = ½ nucleus The second (B) is a triplet due to two equal I = ½ nucleus The third (C) is again a two-fold split due to one I = ½ nucleus The fourth (D) is a triplet due to a I = 1 nucleus

66 Hyperfine Patterns Simulations Not Enough Orientations 9) B-min: 3100 gauss, B-max: 3700 gauss. For Co: A-value = 50 G, for nitrogen: A-value = 20 G, for hydrogen: A-value = 10 G Dimethyl Nitroxyl Radical. Simulations Not Enough Orientations Frequency = MHz, B-min = 3380 gauss, B-max = 3580 gauss. g = 2.005, W = 0.7, A N = 17.0 (1x), A H = 14.8 (6x) To get the pattern right A N needs to be just a bit larger than A H

67 2Fe Ferredoxin Cp 2Fe Fd Cobalamin 2.3 X-band Cp2Fe_spec simulation Field (mt) Q-band /3005/4005 G xyz : , , W xyz : 9, 13.5, Field (Gauss) g xyz = 2.275, 2.220, and W xyz = 25, 25, and 7.0 A Co xyz = 11, 11, and 111 = 18, 18, and 18 A N xyz Overshoot Simulations Overshoot

68 Hyperfine Interactions Simulations 4 x S=1 In this structure the interaction with four nitrogen ligands (I = 1) would result in 9 superhyperfine lines. 269 MCRox1 g xyz = , , and W xyz = 3.5, 4.0, and 4.0 A N xyz = 8.0, 9.7, and 9.7 MCRred1 g xyz = , , and W xyz = 4.5, 3.5, and 5.0 A N xyz = 8.8, 9.9, and Simulations d (Gauss)