Welcome to all the participants

Transcription

1 Homi Bhabha Centenary School on Relaxation in NMR and Related Aspects February 16-20, 2009 National Facility for High-Field NMR, TIFR Welcome to all the participants

2 Relaxation References A. Abragam: Principles of Nuclear Spin Magnetism C. P. Slichter: Principles of Magnetic Resonance A. G. Redfied: Adv. Magn. Reson., 1, 1, 1961 L. Werbelow and D. M. Grant: Adv. Magn. Reson., 9, 189, 1977 N. Murali and V. V. Krishnan, Conc. Magn. Reson., 17, 86, 2003 (A primer in nuclear magnetic relaxation in liquids)

3 Paramagnetic Relaxation P. K. Madhu Dept. of Chemical Sciences TIFR February 18, 2009

4 How complicated it all is An example (without eqution) of the hyperfine relaxation IS-dipolar n e τ rotation τ τ r r < τ > τ e e In solution IS-dipolar IS-scalar complex τ τ r r < τ e > τ ; τ e ; τ l l > τ < τ r r e-e interactions τ lifetime Curie spins The solvent itself τ translational

5 Relaxation Mechanisms in NMR Chemical shift anisotropy Scalar coupling Dipole-dipole coupling Quadrupole coupling Spin rotation M Rel A =CSA M +DD AX +DD AM A X Relaxation pathways are treated independently Simultaneous presence of them is not considered

6 What are Cross-Correlations? Independent existence Relaxation pathways Simulatneous presence Autocorrelation Crosscorrelation Affects T 1, T 2, and NOE M Causes differential effect/multiplet effect among the various transitions A X Rel A =CSA M +DD AX +DD AM + CSA M XDD AX + CSA M XDD AM + DD AX XDD AM

7 Cross-Correlations: Are They Useful? The differential effects coming from cross-terms of CSA with DD or DD with DD may be exploited to get local structural information, such as distances, bond angles, and torsion angles The differential effects may also be used to increase the apparent resolution of a multi-dimensional spectrum of large molecules, TROSY Anil Kumar et al. Prog. NMR Specy. 37, 191, 319, 2000

8 Manifestation of Cross-Correlations Auto-correlation Cross-correlation Single-spin magnetisation modes (total magnetisation of a spin), A z, M z, X z Multi-spin magnetisation modes A z, M z, X z, 2A z M z, 2A z X z, 2M z X z, 4A z M z X z They reflect the difference in the intensity of various transitions of a spin M CSAXDD, Δ A AM, ΔA AX.. DDXDD, δ AM AX... A X

9 Applications of Cross-Correlations DLB and longitudinal multi-spin orders Determine the absolute sign of the various spin couplings Position the principal axes of the spin interaction Evolution of multi-spin orders being sensitive to motional anisotropies can be used to study highly anisotropic systems where conventional NMR relaxation studies normally would not work Detailed description of molecular dynamics and anisotropic interactions at the molecular level Measurement of various structural parameters Increasing the resolution of multi-dimensional spectra

10 Cross-Correlations and Geometry Relative orientation of the anisotropic Interactions and their motions Cross-correlation spectral densities Rotational correlation time of the molecule The order parameter, S 2, hence, dynamics CSAXCSA cross-correlation J ij ( ω) ( Δσi )( Δσ j ) (3cos θij 1) f( τc ) 1 1 ( ω) ( Δσ ) (3cos θ 1) f( τ ) CSAXDD cross-correlation 2 J iij, i iij, c 3 2 rij DDXDD cross-correlation J ( ω) (3cos θ 1) f( τ ) 2 ij, il ij, il c rij ril r ij θij,il r il

11 Relaxation Mechanisms in Paramagnetic Systems Nuclear relaxation processes of paramagnetic complexes: The slow-motion case, A. J. Vega, D. Fiat, Mol. Phys., 31, 347, 1976 Nuclear relaxation in macromolecules by paramagnetic ions: A novel mechanism, M. Gueron, J. Magn. Reson., 19, 58, 1975 Solution NMR of paramagnetic molecules, I. Bertini, C. Luchinat, G. Parigi, Current methods in inorganic Chemistry, Vol. 2, Elsevier, 2002 Papers by La Mar.

12 Paramagnetic Effects Quantitative expressions available for paramagnetic relaxation Paramagnetic metal ions cause shifts of the resonances (could be used to resolve overlapping NMR signals) Enhanced nuclear spin relaxation, PRE Molecular alignment in the magnetic field Various cross-correlation effects Paramagnetic shifts convey useful long-range structural information and can be measured with high accuracy Structure determination of paramagnetic metalloproteins

13 Paramagnetism Paramagnetism associated with unpaired electrons A paramagnetic centre may be also introduced exogenously, spin labels The magnetic moment due to unpaired electrons μ [ ( 1)] S = gμb S S + 1/ for free electrons Essentially the electron-nuclear interaction similar to nuclear spin-spin interaction, except that the electronic magnetic moment is much higher

14 Electron Around the Nuclear Spin Fast molecular reorientation with respect to the g-anisotropy

15 Electron Around the Paired Electron Spins

16 Relaxation also by the fluctuation of the average electron moment by the molecular rotation: Curie spin relaxation (CSR) How Does Nuclear Spin Sense Electron Spin? Electron spins relax faster than the nuclear spin Nuclear spins in each M I level see one electron rapidly changing its orientation among its M S levels and they see an average electron magnetic moment The average electron moment can influence the nuclear energy levels: Local field then fluctuates with a correlation time T 1e The dipolar interaction between electron and nuclear spins is zero when the electron induced magnetic moment is orientation independent and non-zero otherwise A fraction of the electron spins sit on the resonating nucleus leading to a direct shielding constant: Contact term Relaxation can be caused by the fluctuation of the interaction energy, T 1e

17 Nuclear-Electron Interaction The interaction between a nuclear spin and an unpaired electron is termed as hyperfine coupling H = I. AS. A is the hyperfine coupling tensor H Ω = I + Q K D Ω ( ) ω (2) (2) (2) 0 z μ ν μν ( ) l, μν,

18 Chemical Shifts in Paramagnetic Molecules The average induced electron magnetic moment gives a contribution to the chemical shift called the hyperfine shift Direct delocalisation of the electron spin at various nuclear spin sites Effect arising from the anisotropy of the g-tensor of the electron spin Contact shift (Fermi contact term) Pseudo-contact shift (dipolar term) Due to the spin density on the resonating nucleus Due to the spin density outside of the nucleus (more useful)

19 Fermi Contact Coupling and Pseudo-Contact Shift The contact shift arises from the additional magnetic field generated at the site of the nuclear spin by the electron magnetic moment located at the nuclear spin itself. This magnetic moment arises from the electron spin density at the nucleus, weighted by <S z >. The PCS arises from the spin density distribution all over the space around the nuclear spin. This is dipolar in nature, and has useful structural information.

20 Electron Spin Density The unpaired electron is not localised on a single point, but delocalised on the entire molecule. Hence, in every point of space, where the molecular orbital containing the unpaired electron has a non-zero value, the average electron magnetic moment sensed by the nuclear spin is non-zero and proportional to <S z > times the fraction of unpaired electron present at that point. Such a fraction is called spin density which for a single electron is given by the square of its wave function at that point.

21 δ con + δ pc δ con Expressions A geμbs( S + 1) A = = < Sz > 3γ kt γ B I I 0 1 δ pc = χ χ θ 3 12π r 2 ( )(3cos 1) (Isotropic dipolar shift- The contribution to this shift is isotropic Pseudo-contact shift has a square dependence on B 0, hence the shifts may be larger in higher magnetic fields

22 Pseudo-Contact Shift Isotropic electron magnetic moment, isotropic susceptibility, pseudocontact shift goes to zero If the induced magnetic field changes intensity with the molecular orientation sue to the susceptibility being anisotropic, PCS is not zero

23 Expressions

24 Spectra

25 Separation of Contact and PC Shifts

26 Electron Induced Nuclear Spin Relaxation The sole presence of an unpaired electron spin causes nuclear spin relaxation The correlation times for the electron-nucleus interaction? Equations for dipolar and contact interaction mediated nuclear spin relaxation? Can any of these relaxation pathways cross-correlate with the other nuclear relaxation mechanisms?

27 Electron Induced Nuclear Spin Relaxation The magnetic nucleus does not see unpaired electrons as localised but as spin density distributed throughout the space The spin density, in every unit volume, will spend more time in the low Zeeman energy level(s) and less time in the upper levels Changes in the M s values involve changes in the orientation of the electron magnetic moment The time sharing of the levels occurs through electron relaxation Electron relaxation thus provides fluctuating magnetic fields causing nuclear spin relaxation Nuclear spin relaxation due to electrons is contact in origin if reference is made to spin density at the resonating nucleus The rest of the electron density and associated electron relaxation is sensed by the nucleus through dipolar coupling- This relaxation is dipolar in origin

28 Paramagnetic Relaxation Enhancements: PRE Nuclear spin relaxation due to electron relaxation Fluctuation of the electron dipolar field at the nucleus due to the electron relaxation-dipolar in origin There are other mechanisms for nuclear spin relaxation besides electron relaxation

29 Paramagnetic Relaxation Enhancements: PRE Nuclear spin relaxation due to molecular rotation Rotation of the molecular frame causes the nucleus to see the electron in different positions. If the rotation is faster than the electron relaxation time, on the rotational time scale the nucleus sees the electron with the same M S value but on different positions in space. This random motion of the electron around the nucleus can be again seen as a fluctuating magnetic field that causes nuclear relaxation via dipolar coupling. In fact, the nucleus sees the induced electronic magnetic moment <m> aligned along the magnetic field. Upon rotation, this average moment can cause fluctuating magnetic fields sensed by the nucleus through space. This is also dipolar, called Curie spin relaxation (CSR).

30 Paramagnetic Relaxation Enhancements: PRE Nuclear spin relaxation due to chemical exchange The binding and detachment of a moiety containing the resonating nucleus and unpaired electron (chemical exchange) can cause fluctuating magnetic fields at the nucleus through both contact and dipolar mechanisms

31 Paramagnetic Relaxation Enhancements: PRE Relaxation measurements- Information on the interaction between nuclei and unpaired electrons and time dependence of the interaction parameters Dipolar coupling: Electron-nucleus distance, and structural information Contact interaction: Unpaired electron spin density on the various resonating nuclei and hence to the topology (via chemical bonds) and the electronic structure of the molecule We need to decouple these mechanisms to get useful information

32 Correlation Times

33 Paramagnetic Relaxation Enhancements: PRE The longitudinal relaxation enhancement of the nuclear spin due to a coupling with the unpaired electron Time-independent Zeeman fields Time dependent electronic field seen by the nucleus The fluctuation of this causes nuclear spin relaxation

34 Modulation of Hyperfine Interaction Nuclear spin relaxation through the modulation of the hyperfine coupling Dipolar term Contact term

35 Dipolar Relaxation Mechanisms Consider only the dipolar relaxation (due to relevant structural information content) Even here, there are two sources for the fluctuations: The relaxation of the electron spin S, dipolar/solomon The motion of r We can write S=S C +s where S C is the thermal average of S, called the Curie spin S C is aligned along the magnetic field B 0 such that geμbb0 S( S + 1) (high-temperature approx.) < Sz >= SC = 3γ kt I

36 Curie Spin Relaxation (CSR) CSR in the interaction between the nuclear spin and the static magnetic moment <S z > (the time-averaged electron spin moment) This interaction cannot be modulated by the electron spin relaxation, since <S z > is already an average over the electron spin states The correlation time for this coupling is only determined by τ ρ This relaxation mechanism is called the magnetic susceptibility or CSR (to reflect its relationship with the magnetic susceptibility of a sample via Curie law)

37 I-S Spin System: Energy Levels, W s, Transition Frequencies

38 Relaxation Expressions: Solomon Term Nuclear relaxation times, 1/T 1 and 1/T 2 Here, = + τ τ T s1 c 1e = + τ τ T s2 c 2e and ω I << ω In the fast motion limit, ω S and ω I <<1/τ c ), absence of chemical exchange, and T 1e =T 2e S This is the qualitative statement that the shorter the electronic relaxation times, smaller the paramagnetic effects on nuclear relaxation

39 Paramagnetic Relaxation Enhancements: PRE Fast relaxing electrons: PRE is smaller, nuclear spins can be studied with NMR Slow relaxing electrons: PRE is larger, severe line broadening for the nuclear resonances Ideally we need fast relaxing electrons, PRE negligible, and T 1e, T 2e effects can be neglected leading to only CSR

40 Relaxation Expressions: Contact Term Only flip-flop terms are active In the fast motion limit,

41 Relaxation Expressions: CSR

42 Curie Spin Relaxation (CSR) CSR is significant when the dipolar coupling described by the Solomon s equations is governed by the electronic relaxation times, T e <<τ c = + τ τ T s1 c 1e Efficient relaxation-long correlation times-large T 1e - Slow electronic relaxation Use of ions like Mn 2+ or Gd 3+ CSR may be neglected But one should know T 1e and this is difficult On the other hand use ions with short T 1e, fast electronic relaxation, then CSR broadening is overwhelming, and only rotational correlation times need to be considered CSR increases with magnetic field and the size of molecules Use of ions such as high-spin Fe 2+ (S=2) as in hemoglobin or rare earth Ions which have short T 1e.

43 Relaxation Mechanisms in NMR Chemical shift anisotropy Scalar coupling Dipole-dipole coupling Quadrupole coupling Spin rotation electron Curie spin relaxation M Rel A =CSA M +DD AX +DD AM +CSR Ae A X Relaxation pathways are treated independently Simultaneous presence of them is not considered

44 Geometry Relative to Paramagnetic Centre r e N es S Θ N esi rn H rr e H ei r IS Θ H eis I I

45 Geometric Dependence of the Dipolar Effects Involving an Electronic Spin Pseudocontact shift χ z θ I e r Relaxation χ x ϕ χ y I r e Interference with nucleus- nucleus dipolar relaxation e r I θ K

46 Differential Narrowing in a 2D Multiplet anti-trosy (αα) semi-trosy 2 (αβ) semi-trosy 1 (βα) TROSY (ββ)

47 TROSY in Paramagnetic Proteins TROSY has enabled NMR of very large proteins of ca amino acid residues long Higher magnetic fields of MHz are required to see the manifestation of TROSY effects TROSY effects may be more evident in paramagnetic proteins due to additional cross-correlations, CSA*DD+DD*DD+CSR*DD TROSY in paramagnetic proteins will have directional information as CSR is geometry dependent with respect to the electron For all practical purposes, CSRXDD cross correlation Is like CSAXDD cross correlation Hence similar effects, such as in TROSY, can be expected

48 Angular Dependence in 2D Multiplet Effect S I S I S I S I S I

49 PIN Geometry Dial Paramagnetic Induced Narrowing Muller, Otting, Brutscher

50 TROSY vs HSQC, Myoglobin TROSY HSQC

51 Coupled HN-HSQC: Myoglobin Madhu et al., J. Biomol. NMR 20, (2001)

52 Cross-Correlation Effects: Overlay of 4 αβ-hsqc-αβ

53 CSR: Structure Elucidation Long-range information possible Ferrocytochrome, S=2 Boisbouvier.Brutscher..,JACS, 121, 7700, 1999

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55 Sperm Whale Myoglobin (153 Residues) Fe (II) S=0 Fe (III) S=1/2 Fe (III) S=5/2

56 Two Distance Shells from the Metal can be Studied in the Two Spin Samples CN-Mb F-Mb 7 Å < r HFe < 11 Å 10 Å < r HFe < 25 Å

57 PCS and Susceptibility Anisotropy

58 Line Shapes and Pulse Sequence

59 Quantitative Evaluation isotropic case

60 Anisotropy of the Magnetic Susceptibility Tensor Isotropic χ-tensor - Axially symmetric dipolar shift tensor Anisotropic χ-tensor - rhombic dipolar shift tensor σ DSA σ DSA High spin Low spin

61 Anisotropic Magnetic Susceptibility isotropic susceptibility axial DSA anisotropic susceptibility non-axial DSA

62 Quantitative Evaluation H z θ Z HN N anisotropic case x θ X HN y θ Y HN

63 Angular Dependence of the Cross-Correlation Rates Isotropic magnetic susceptibility Anisotropic magnetic susceptibility θ zhfe = 0 θ zhfe = 90 HN within xz plane HN normal to xz plane

64 CSR Cross-Correlation Data Complete assignment of myoglobin in the lowspin and high- spin states Distance measurements possible upto 11 A in low- spin state and 25 A in high- spin state Systematic study of the contribution of the g- possible tensor made Both diamagnetic and paramagnetic samples needed for getting pure cross-correlation contribution and quantification of model Assignment of paramagnetic proteins will be possible by monitoring only cross-correlated relaxation without any NOE constraints

65 Identification of solvent exposed regions of a protein: Useful for the detection of intermolecular contact sites in protein-ligand complexes and protein-multimers

66 Effect of Paramagnetic Additives on the NMR Parameters of the Protein (in Particular its 1 H Relaxation Times) 1. TEMPOL Gadolinium complexes feature a STRONGER paramagnetism Gd(DTPA- BMA) Omniscan (Gadolinium diethylentriamine pentaacetic acid bismethylamide) Both are uncharged and highly water soluble lower concentrations are required 2. Gd(DTPA-BMA) is less hydrophobic than TEMPOL 3. Gd(DTPA-BMA) stable over a wide range of ph and against redox-active compounds in solution the binding potential to proteins is minimized Ideal binding agent

67 Effect of Paramagnetic Additives on the NMR Parameters of the Protein (in Particular its 1 H Relaxation Times) The absence of binding of Gd(DTPA-BMA) was confirmed using: Resonances were attenuated, but none disappeared No significant chemical shift changes observed upon the addition of the relaxation agent In the absence of specific binding, the paramagnetic agent is expected to enhance the relaxation rate of the protein protons as a function of their solvent exposure and distance from the surface

68 Effect on Ubiquitin Proton Resonances Relaxation enhancements are reliably big for highly surface exposed protons and small for the deeply buried ones 0 mm Omniscan 4 mm Omniscan largely affected resonances slightly affected protons

69 Quantitative Description of the Relaxation Enhancements Relaxation agent is non-specific, yet rotationally correlated, complex with the protein, and the dipolar coupling between the electron spin and 1 H spin is modualted by τ r, T 1e, and τ M 1. Second-sphere relaxation position independent relaxation time τ c Life time of the intermolecular adduct Bertini, I.. et al. Nuclear and electron relaxation; VCH, Weinheim, 1991.

70 Second-Sphere Interaction Mode Omniscan TEMPOL

71 locations protected from access to Omniscan although significantly solvent exposed in the NMR structure criteria for the identification of the dimerization site

72 Conclusions correlations between spectral and structural features Omniscan signals of the HSQC are affected proportionally to their solvent exposure Myoglobin assignment can be performed with only the 3D NOESY-HSQC using : crystal structure diamagnetic assignment estimates on the χ tensor depending on the metal spin, CSR-DD cross-correlation Is measurable at different distance shells from the metal the effect of anisotropic magnetic susceptibility can deeply affect the use of the cross-correlated relaxation rates

73 Lanthanide Ions for Structure Determination The paramagnetism of Lanthanide ions useful for fast 3D structure determination protein-ligand complexes Combination of PCS induced by a site-specifically bound lanthanide ion and prior knowledge of the 3D strucutre of the La-labelled protein can be used to achieve Rapid assignment of the NMR spectra Structure determinations of protein-protein complexes Identification of the binding mode of low-molecular weight compounds in complexes with proteins

74 Lanthanide Ions for Structure Determination Lanthanide ions are attractive due to their relatively large paramagnetic effects which are also varied These could be nice targets in the study of large protein-protein complexes which are other difficult to study with NMR or X-ray Lanthanides also have no known essential role in biology Ca 2+ ions, for instance, in calcium binding proteins may be replaced with lanthanide ions embedding the lanthanide ion in a rigid and extended molecular framework of defined 3D structure (the ionic radii of Ca and La ions are nearly the same)

75 Pseudocontact Shift 2 3 ( 3cos ϑ 1) + Δχ sin ϑ cos 1 2 pc δ = Δχ 2ϕ 3 ax rh 12π r 2 χ z θ I χ x e ϕ r χ y Orientation dependence Long-range information

76 Pseudocontact Shift Protein complex with La 3+ and Tb 3+

77 PCS Isosurfaces

78 Most Common Paramagnetic Metals in Biomolecular NMRc

79 Most Common Paramagnetic Metals From the d-transition

80 Attachment of a Lanthanide Binding Site in a Protein (a) Replacement of a pre-existing calcium binding site (Bertini et al., J. Am. Chem. Soc., 2001, 123, (b) site-specific derivatization of a free Cys thiol with a lanthanide-complexing agent (Dvoretsky et al., FEBS Lett., 2002, 528, 189; Ikegami et al., J. Biomol. NMR, 2004, 29, 339), Purdy et al., Acta Crystallogr. D, 2002, 58, (c) design of fusion proteins with lanthanide-binding motifs EF-hands (Ma and Opella, J. Magn. Reson., 2000, 146, 381) calmodulin (Feeney et al., J. Biomol. NMR, 2001, 21, 41) combinatorially screened peptides (Wohnert et al., J. Am. Chem. Soc., 2003, 125, 13338)

81 Fast Determination of the Binding Mode of Small Ligand One example: Determination of the 3D structure of a small ligand molecule bound to its protein target in solution Simultaneously, the location and orientation of the ligand molecule with respect to the protein An eg: thymidine bound to ε186/θ loaded with Dy 3+, Tb 3+, or Er 3+

82 Fast Determination of the Binding Mode of Small Ligands M. John, G. Pintacuda, A.-Y. Park, N. E. Dixon and G. Otting J. Am. Chem. Soc., 2006, 128,

83 Lanthanide Labeling: Advantages

84 Lanthanide Labeling: Advantages

85 Fast Determination of the Binding Mode of Small Ligands Concentration-dependent relaxation enhancements and PCS lead to binding affinity and the fraction of bound thymidine From the PCS data of thymidine, the position of 1 H and 13 C can be positioned with respect to the Δχ tensor and the ε186 molecule The structure and the location of the thymidine molecule was found to be similar to that determined in single crystal studies

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87 Further CSRXDD Cross-Correlation Effects