Pulsed Dipolar EPR Spectroscopy

Transcription

1 Pulsed Dipolar EPR Spectroscopy Maxim Yulikov (Zurich, Switzerland) V International School for Young Scientists Magnetic Resonance and Magnetic Phenomena in Chemical and Biological Physics September 5-2, 28, St. Petersburg region, Russia

2 Two-spin system and the electron-electron coupling Like spins /2 (two electrons) A B Weak coupling dd dd ^ ^ C,D ^ ^ C,D ^ A B B A B ^^ ^ ^ E F C,D ^ ^ C,D H = A S Az + S + B Bz H dd + J( S xix+ S yiy+ S ziz) S I + S I = ½( S I + S I ) x x y y A Strong coupling dd dd B A B Dipolar alphabet A B secular non-secular pseudo-secular non-secular non-secular non-secular B: Many slides are the courtesy of Prof. Gunnar Jeschke (ETH Zurich)

3 Two-spin system and the electron-electron coupling Electron-electron magnetic dipolar interaction depends on the spin-spin distance, orientation of the spin-spin vector with respect to the magnetic field, and some fundamental constants. This makes dipolar interaction a perfect reporter about the molecular structure. Exchange interaction does depend on the spin-spin distance, but this dependence is much more complicated, strongly system dependent, and its determination with any accuracy requires expensive quantum chemistry calculations. It is most convenient to measure spin-spin interactions in the absence of exchange. Further simplifications can be made if dipole-dipole interaction is weak, compared to the resonance frequency offset between A and B spins. Then, only the secular term in the dipolar alphabet makes a significant contribution to the energy levels and to the spin density time evolution. Dipolar alphabet secular pseudo-secular non-secular non-secular non-secular non-secular

4 rigin of the Pake pattern B circumference: 2 sin r d H = d 2S I ½ dd r 2 3cos g h 3 4 zz g 2 2 B B observer spin r local field ( ) r P( )

5 Dipole-Dipole Interaction in EPR (secular part) for weak g anisotropy B observer spin local field r nly A term is secular with respect to the electron Zeeman Hamiltonian. B for strong g anisotropy μ r μ 2 ne has to compute, which part of the dipolar interaction is secular with respect to the anystropic electron Zeeman Hamiltonian.

6 Distance measurements by CW EPR vs. PDS Dipolar interacon of aligned spins itroxide EPR spectrum & Pake pa erns B observer spin A CW 8 MHz r Pake pa ern -3 r ESE.5 nm broadening safely visible Dipolar broadening 2 nm 3 nm broadening hardly visible broadening insignificant nm

7 Distance measurements by CW EPR vs. PDS dipole-dipole coupling in a doubly labeled molecule is manifested as line broadening (pseudomodulaon) works well between.3 and.8 nm longer distances: uncertainty from other broadening mechanisms shorter distances: uncertainty from exchange coupling

8 Double-Frequency Experiments: DEER/PELDR (3-pulse) PELDR A. D. Milov, et al. Fiz. Tverd. Tela (Leningrad), 98; A. D. Milov, et al. Chem. Phys. Lett Phase evolution of the spin density matrix due to the dipolar term SAZSBZ is refocused by the blue and by the red -pulse, while the electron Zeeman-induced ( S AZ term) phase evolution is only refocused by the blue -pulse. Thus, at the time point of electron spin echo (ESE), the dipolar evolution time is equal to 2 t. By varying the position of the red pulse, we can modulate the ESE intensity with dipolar frequency. Further experiments were designed to avoid the dead time issue (4-pulse DEER) and to improve the transverse relaxation properties by refocusing (5-pulse and multi-pulse DEER). B: There are several good EPR chapters in the emagres (Enciclopedia of Magnetic Resonance). This Figure is from the chapter Pulse Dipolar Spectroscopy ( G. Jeschke, emagres, 26).

9 Double-Frequency Experiments: DEER/PELDR (3-pulse) PELDR FURTHER READIG: G. Jeschke Structure & Bonding 22; G. Jeschke emagres 26 A. D. Milov, et al. Fiz. Tverd. Tela (Leningrad), 98; A. D. Milov, et al. Chem. Phys. Lett (4-pulse) DEER Dt ( )/ D() '2+' artefact R. E. Martin, et al. Angew. Chem. Int. Ed. 998; M. Pannier, et al. J. Magn. Reson pulse DEER Ft ( )/ F() P. P. Borbat, et al. J. Phys. Chem. Lett pulse PELDR zero time calibration:. A. Kuznetsov et al. PCCP 29 vercoming zero-time problem: A. D. Milov et al. Appl. Magn. Reson. 2

10 Ultimate resolution by a constant-time experiment if the total length of the pulse sequence changes, dipolar evoluon is damped by relaxaon for distances larger than ~ 3-4 nm, dipolar modulaon is overdamped 2 T e 2 r = 4.5 nm T 2= μs Keep fixed, vary only t, pulse sequence has constant length 2 3 t (μs) 4 5 () mw /2 deadme r = 4.5 nm constant me (2) mw t 2 3 t (μs) 4 5

11 -pulse DEER Double-Frequency Experiments P. P. Borbat, et al. J. Phys. Chem. Lett. 23 The 5-pulse DEER experiment demonstrates superior relaxation properties, as compared to the 4-pulse DEER. f course, the corresponding increase of the detectable distance range is not so large, due to the r -3 law. More pulses create more evolution pathways, and some of them lead to dipolar-modulated echoes too. Rigorous analysis of artefacts and their suppression in the 5-pulse DEER can be found in the two tandem publications of F. Breitgoff, et al. in Phys. Chem. Chem. Phys. 27

12 Information content of the DEER signal Primary experimental data Form factor (intramolecular) Vt ( )/ V().5 intermolecular background (exponential decay) Hex (CH 2 ) 6 Me Hex (CH 2 ) 6 Me background correction F(t).8.6 / ( r 3 ) umber of spins in the object 5 t (μs) t (μs) Dipole-dipole interaction Dipolar frequency d r g h 3 4 g 2 2 ( 3cos ) 2 B decay envelope depends on distance distribution: fast decay of modulation broad distribution Form factor of an isolated spin pair F ( r, t) V( t) V() 2 ( ) [ 2d( r) t] { cos } sind modulation depth depends on pump pulse inversion efficiency rientation dependence of inversion efficiency is neglected in standard data analysis programs

13 Average distance and distance distribution Molecular dynamics causes distribution of r Expectation: r max Hex Hex Hex Hex Hex Hex Hex Hex bent, higher energy, lower population, smaller r stretched, min. energy, max. population, max. r Experimental distance distribution Dt () Tikhonov regularization Pr () r (nm) G. Jeschke, A. Koch, U. Jonas, A. Godt A, J. Magn. Reson. 55, (22) G. Jeschke et al. Appl. Magn. Reson. 3, (26) Basic mathematics fit simulated dipolar evolution function St ()= K Pr () Minimize, under the restraint Pr ( ), G d ( P) KP r 2 dr 2 r D t P mean square deviation regularization parameter a 2 2 roughness nd of 2 derivative

14 Why regularization is required and how to do it Hex Hex Hex Hex Hex Hex Hex Hex too small optimum too large Vt ().8 Vt ().8 Vt ().8 oversmoothed t (µs) t (µs) t (µs).4 undersmoothed.4.2 Pr ().2 Pr ().2 Pr () r (nm) r (nm) r (nm) consequence of an ill-posed problem for detailed discussion, see: G. Jeschke, in Structure and Bonding (Eds. C. Timmel and J. Harmer), 22, DI:.7/43_2_6

15 L curve criterion for selecting regularization parameter Example: PutP 9/37 log = -3 = 3 = log not foolproof: L curve itself subject to errors (noise, background correction) Dt () t (μs) x -3 Pr () 5 r = 2.82 nm?? r (nm) see also: Y. W. C HIAG, P. P. B RBAT, J. H. FREED, J. Magn. Reson. 25, 72, Additional validation (here test of background correction) variation of background dimenison D = [.8,2.2] (5 equidistant values) variation of modulation depth x insignificant! = [.45,.5] ( equidistant values) variation of background decay constant k = [.8,.22] ( equidistant values) Pr () r (nm) r (nm) implemented in DeerAnalysis29:

16 Limitations of Tikhonov regularization Boxcar [2.,4.] nm Sawtooth Simulated data L curve Distance distribution Vt () t (μs) log log Pr () 8 4 original r (nm) steep flanks, flat top smoothed out [2.,4.] nm Vt ().6 log -5-2 Pr () 5 cusp smoothed out Two Gaussians (broad/narrow) 2 t (μs) log r (nm) r = 3.5 nm (r ) =.5 nm r 2 = 3. nm (r ) =.2 nm 2 Vt () t (μs) log log r (nm) narrow feature broadened broad feature rugged see also: G. J ESCHKE, G. P AEK, A. G DT, A. B EDER, H. PAULSE, Appl. Magn. Reson. 24, 26,

17 rientation selection in DEER experiments EPR spectrum of a SL is often anisotropic. Thus, if the molecular frame is fixed with respect to the spin-spin vector (rigid molecule), then the excited orientation of the spin-spin vector depends on the spectral positions for the A and B spins. This forms the basis for the orientation selection PDS. A. M. Bowen et al., Struct. Bond., 24 see also G. Jeschke, emagres, 26

18 rientation selection in DEER experiments (example rigid ruler) Y. Polyhach et al., J. Magn. Reson., 27

19 rientation selection in DEER experiments (example DA) DA double helix is a rather conservative structure, and it allows incorporating a rigid SL, which pairs to guanine, instead of cytosine. In this case, orientation selection in DEER allows to determine the model for DA flexibility. Guanin A. Marko et al., Phys. Rev. E, 2

20 eglect or averaging of orientation selection broad conformational distribution of nitroxide labels averages orientation selection at X- and Q-band frequencies (9- GHz) II III for metal centers with strong g anisotropy (Cu, Fe, etc.), orientation selection is significant at high field/frequency (W-band or higher) it may be more significant beware if conformational space of nitroxide label is strongly restricted (narrow distance distribution) Minimizing orientation selection by a field sweep Hex Hex Hex Hex pump ( 2 ) observe ( ) with field sweep without field sweep with field sweep sweep width: 37 G (X-band) B dip ( MHz) - dip ( MHz) increment: G (X-band) traces are summed Hex Hex (CH 2 ) 6 Me (CH 2 ) 6 Me

21 Improving data quality The longer the distance, the longer t max should be The longer the t max is, the worse is signal-to-noise ratio t max (µs) /2 reliable distance measurement ( r, ( r)) r (nm) 2 2 t below this line: suppression of long distances by background correction G. J ESCHKE, Y E. PLYHACH, Phys. Chem. Chem. Phys.. 27, 9, t max < 2 T [ms] DEER signal is attenuated by constant factor { } exp -2( + )/ T prolonging 2 2 prolonging T vastly improves data quality T leads to lower repetition rate, S/ decreases unless overcompensated by gain in Boltzmann factor T [K] T 2 limit T 2 [ s] T [K] T 2 limit is set by hyperfine fluctuations, usually by proton spin diffusion deuteration of matrix improves T 2 limit S/ [a.u.] optimum temperature For t max versus S/ compromise, see: G. JESCHKE, in Structure and Bonding (Eds. C. Timmel and J. Harmer), 22, DI:.7/43_2_6 see also: G. JESCHKE, Annu. Rev. Phys. Chem. 22, 63,

22 Excitation profile of a rectangular /2 pulse Side-bands of the excitation profile of the m.w. pulse would overlap with the other pulse (at the second frequency) in the DEER experiment. As a result we get ESEEM and 2+ artefacts.

23 Avoiding artifacts from nuclear modulation /2 forbidden observer spin transition () mw (2) mw 2 t pump pulse excites observer spins pump ( 2) 65 MHz 4 MH z observe ( ) Average nuclear modulation by varying phase of electron dipole-dipole modulation does not depend on phase of nuclear modulation does depend on averaging over ( = 8 ns, 8 steps for H, 2 = 56 ns, 8 steps for H) will partially cancel nuclear modulation artifact peaks in Pr ( ) due to residual nuclear modulation possible "Distance analysis" of H ESEEM Vt () 2 H at Q-band.87 nm artifact t (μs).9.8 X band! "Distance analysis" of 2 H ESEEM t (μs).5 2 r (nm) r (nm)

24 Multi-spin contributions in the DEER time evolution signal The conventional form of the dipolar evolution signal is only detected, if there are isolated spin pairs in the sample. This means, each molecule must contain exactly two spin labels, and intermolecular distances must be much longer than the intramolecular spin-spin distances. If more than two spins are present within a molecule or, eg.. there is a complex formed by several molecules, then the product rule (on the right) applies. This leads to the combinations of dipolar frequencies, which need to be analised in a special way.

25 Suppression of multi-spin "ghost" contributions by power scaling What are ghost contributions? F(t) t [ s].5 P(r) Experimental test for a triradical simulation input biradical, =2 triradical, =3 tetraradical, = r [nm] r [nm] T. von Hagens, Y. Polyhach, M. Sajid, A. Godt, G. Jeschke, PCCP 23 P(r) from Ft ( ) from F /2 What is power scaling? form factor Ft ( ) is raised to power /( -) before subtraction of constant part and Tikhonov regularization F (t) F (t) Planar tetraradical without power scaling nm =.6 =.4 =.2 pair t [ s] Planar tetraradical with power scaling =.6 =.4 =.2 pair t [ s] =.6 =.4 =.2 pair r [nm] =.6 =.4 =.2 pair r [nm]

26 Single-Frequency Experiments Six-pulse version of the DQC experiment S. Saxena and J. H. Freed Chem. Phys. Lett. 996; J. Chem. Phys. 997; P.P. Borbat and J. H. Freed Chem. Phys. Lett rectang. SIFTER Four-pulse version of the SIFTER experiment solid echo rectang. DEER Five-pulse version of the SIFTER experiment broad-band SIFTER Jeener-Broekaert echo G. Jeschke, M. Pannier, A. Godt, H. W. Spiess Chem. Phys. Lett. 2 P. Schöps,... T. F. Prisner J. Magn. Reson. 25

27 Single-Frequency Experiments The 2+ pulse experiment t ot very much in use: - rather low sensitivity - complicated dipolar evolution function for large - interference of falling and rising dipolar evolution signals - complex background behavior - strong ESEEM contributions A. Raitsimring Biol. Magn. Reson. 2 General remarks: Single-frequency PDS experiments are of particular practical interest to measure distances between radicals with narrow EPR spectrum (e.g. Trityl, BDPA). In the last few years, due to the development of broad-band chirp pulses setups, the efficient use of single frequency techniques for nitroxide SLs became possible. The '2+' effect is an important source of artefacts in the two-frequency experiments, whenever pulse's excitation bands overlap. Its practical applications as a distance determination technique are currently quite limited.

28 The RIDME pulse experiments Single-Frequency Experiments 3-pulse RIDME DEER (pump) RIDME Example: Gd(III)-Gd(III) RIDME 4-pulse RIDME Intensity [a.u.] DEER (observe) 5-pulse RIDME B [T] DEER L. V. Kulik et al. Chem. Phys. Lett. 2; S. Milikisyants et al. J. Magn. Reson. 29 RIDME experiment utilizes fast longitudinal relaxation of B spins ( but not too fast, to not average it out! ). If during the mixing block the B spin flips with a substantial probability P, this block acts, with respect to the dipolar evolution, as an effective pump pulse of inversion efficiency P. RIDME t t T mix S. Razzaghi, et al. J. Phys. Chem. Lett. 24 t

29 Theoretical Description of the RIDME Background RIDME pulse sequence t T mix t t t 2 t 3 M( z t, ) M( x t, ) M x( t, ) M x( t2, ) M( z t, ) i t i i t i Transferring one component of the transverse magnetization to the z-direction creates a non-equilibrium "polarization grid", which can be shifted left or right by the flip of the B spin, or can be smeared out by the spectral diffusion processes during the mixing block i t i

30 RIDME spectroscopy with metal centers High-spin case: 2 a + Gd B R = R local field R 2- R R Gd R R inverted local field pulse or S z +7/2 +5/2 +3/2 +/2 -/2-3/2-5/2-7/2 Gd( III) centers in magnetic field: energy levels, neglecting ZFS, and dipolar patterns. Amplitude [a.u.] 5 5 Frequency [ MHz] n= n=2 n=3 n=4 n=5 n=6 n=7 relaxation Spin A (observer) Spin B First Gd( III) RIDME results see in S. Razzaghi et al. J. Phys. Chem. Lett. 24

31 RIDME spectroscopy with metal centers fit the correct background dimensionality account for higher harmonics by choosing properp 2 and P3 values PyMTA.Gd-3.4nm-PyMTA.Gd: 6 μ s, 2K K. Keller et al. PCCP 27

32 RIDME spectroscopy with metal centers Gd( III)-Gd( III) RIDME data analysis with calibrated kernel St ( )/ S max Ft ( )/ F max t/ μs t/ μs d/ nm. pd ( )/p max 6 nm 3.4:4.7 nm 4.7 nm 4.3 nm 3.4 nm 3 nm K. Keller et al. PCCP 27 In general, RIDME experiment works well with paramagnetic metal centers, where the EPR spectrum is broad and longitudinal relaxation is not much slower (optimally, from five to ten times slower) than the transverse relaxation. This can be also measured in the radical-metal pairs. ote that then one needs to consider transverse relaxation of the detected A spins (typically, radicals) and longitudinal relaxation of the'pumped' by relaxation B spins (typically, metal centers).

33 ESEEM artefacts in the RIDME data Suppression by division or by use of soft pulses A good overview of the division methods can be found in: D. Abdullin et al. J. Phys. Chem. B, 25

34 ESEEM artefacts in the RIDME data Suppression by averaging over delay time variations K. Keller et al. JMR 26 St ( ) Ft ( ) Pd ( ) d 2 [ s] d 2 [ s] d [nm]

35 ESEEM artefacts in the RIDME data RIDME time trace contains also oscillations due to the electron-nuclear interactions. If the amplitude of these, so called ESSEM signals, is small, compared to the overall echo amplitude, they can be rather efficiently averaged out by varying the delay times over the period of these oscillations. If the ESEEM amplitude is very large, this method does not work, and other methods don't work either. Similar, but weaker ESEEM artefacts are often seen in DEER. They can be averaged out in the same way. This is one of the standard DEER measurement protocols. St ( ) Ft ( ) Pd ( ) d 2 [ s] d 2 [ s] d [nm]

36 Lanthanide Ions as Probes in Pulse EPR complexing agent as label variation of lanthanide = variation of spin label possibility of different EPR experiments with different Ln3+ Gd 3+ - r Ln3+ - S = 7/2 - direct detection - Gd3+-Gd3+ DEER at high field A.M. Raitsimring et al., JACS, 27, 29, Gd -nitroxide DEER Lueders et al. J. Phys.Chem. Lett.,2, 2, Dy - S = 5/2 (effective spin /2) - indirect detection - Dy3+-nitroxide T relaxation enhancement in preparation La3+ - S = - diamagentic reference for RE

37 Measurement - r Ln 3+ Principles direct detection Double Electron Electron Resonance (DEER) in Gd-nitroxide pairs obs. pump F(t)/F().8.6 π/2 π π τ τ τ 2 τ 2 t π bs. - Gd(III) pump - nitroxide / dd ( r 3 ) dd t [ µs] = ( r, ) dd (Lueders et al. JPC Lett. 2) B dipolar interaction local field pulse or relaxation inverted local field Spin A (observer) Spin B Methodological advantage: both techniques can be performed on the same system upon exchanging Gd(III) and Dy(III) at the lanthanide binding site. k = C R 6 (Jäger et al. JMR 28) indirect detection Relaxation Enhancement (RE) π π/2 π τ τ 2 τ 2 inversion recovery k [ s ] 3 - bs. - nitroxide fast relaxing - Dy(III) Intensity [a.u.] Dy Lu / La Time k r T[K]

38 Relaxation Enhancement: Theory Dipolar induced relaxation (S=/2; I=/2) If the longitudinal relaxation of the B spins is much faster than inverse of dipole-dipole interaction, then it is averaged to zero, and cannot be detected in DEER, RIDME, DQC or other 'static PDS' experiments. There is, however, contribution to the enhanced relaxation of the A spins (slow, index ' s') in the presence of B spins (fast, index ' f'). This contribution can be analytically computed, in the so-called Redfield regime (the above condition), which leads to a relatively simple formulae for longitudinal ( T) and transverse ( T2) relaxation of the A spins. The values T T correspond to the relaxation of A spins without B spins. and 2

39 Distance constraints from Dy(III)-induced RE RE Dy 3+ In our analysis we use the following assumptions: The functions fb, fcd and feforiginate from corresponding terms in dipolar alphabet and depend on the orientations of the two eigenframes on their resonance frequencies and on the relaxation times of fast relaxing agent. The fast relaxing species can be treated within the Redfield regime. Isotropic g-value (g 2) for the nitroxode radicals and axial symmetry for the Dy(III) g-tensor with principal values: g = 4, g = 4.2. Fast relaxation for Dy(III) witht f = T 2f, which follows an empirical law max Average Relaxivity Approximation, k = C R 6 has been shown to work very well for Dy(III)-nitroxide spin pairs (Jäger et al. JMR 28), All orientations of fast relaxing spin are equally probable.

40 π 3+ Data Processing for the Dy -induced RE RE Dy 3+ π/2 π Inversion Recovery Traces Divided Traces Dy/Lu Intramolecular Intermolecular τ τ 2 τ 2 Inversion Recovery Divided Traces Dy/Lu Background Corrected Trace Intramolecular Relaxation /e Intensity [a.u.] Intensity [a.u.] Intensity [a.u.] Intensity [a.u.] Dy Lu / La Time Time Intramolecular Background (Intermolecular) Time /Δk Time

41 Data Processing for the Dy 3+ -induced RE RE Experimental example: Inversion Recovery Traces Divided Traces Dy/Lu π Dy 3+ π/2 π Intensity [a.u.] Dy Lu Time [milli seconds] Intensity [a.u.] Time [milli seconds] τ τ 2 τ 2 Divided Traces Dy/Lu Background Corrected Trace Inversion Recovery Intensity [a.u.] Intensity [a.u.] 2 3 Time [milli seconds] 2 3 Time [milli seconds]

42 Distance constraints from Dy(III)-induced RE 3 ( ) At the temperature of maximal RE we know the relaxation time of B spins, and then the overall analysis does not depend on any phenomenological constants! T4-lysozyme orthogonally labeled with nitroxide radicals (attached to an unnatural amino-acid) and Ln(III) chelates (attached to a cysteine) 68 ( ) r r 9 ( Dy(III) or Lu(III) ) S 3+ Ln -DTA H Ln 3+ Gd k / s ( Ln) - 3( ) T/ K 2.8 nm 3 - k / s ( Ln) - 68( ) T/ K 3. nm Correspondence between RE and DEER Spin-labeled WALP23 polypeptides incorporated into DPC bilayers DEER: (r ± ) / nm WALP23 T4Lys RE: (r ± Δr) / nm T range / K max * WALP23 T4Lys * * Sample # Ln 3+ DPC bilayer k / s T/ K 2. nm 2.3 nm 2.6 nm 2.9 nm S. Razzaghi et al. ChemBioChem 23; P. Lueders et al. Mol. Phys. 23

43 Multiple Relaxation Pathways Dy The influence of Dy ions and the membrane-dissolved 2 molecules on the relaxation of nitroxide species is not additive! k 2 Dy 3+ 2 La 3+ Relaxation Enhancement in a Three-Spin System A 5-2 Dy 3+ B 8 position - k 2 Dy 3+ k [ s ] Dy 3+ k [ s ] position 5 - k 2 Dy T [K] T [K] P. Lueders, H. Ja ger, M.A. Hemminga, G. Jeschke and M. Yulikov, JPC Letters, 22

44 Relaxation Enhancement: General Remarks Relaxation Enhancement (RE) experiments allow for reliable mean distance determination, which is now also demonstrated experimentally. ote that RE cannot reliably reveal the width of the distance distribution. It is also more restricted with respect to the longest detectable distances, as compared to static experiments, like DEER. Importantly, to avoid any phenomeniological parameters, RE should be measured at the temperature of fastest enhancement. Fortunately, the top of the temperature-dependent RE curve is typically quite flat, and a rather broad temperature range can be tolerated. A complication might arise, if more than one type of B spins enhances the relaxation of A spins. Such contributions are not necessarily additive.