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NMR (PG503)

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NMR (PG503) Solid-state NMR: Anisotropic interactions and how we use them Dr Philip Williamson February 2009 Coherent build-up of CP Dynamics * Coherent build-up of ... – PowerPoint PPT presentation

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Title: NMR (PG503)


1
NMR (PG503)
  • Solid-state NMR Anisotropic interactions and how
    we use them

Dr Philip Williamson February 2009
2
Solid-state NMR spectra
3
Solid-state NMR
  • Anisotropic Interactions
  • What are they, what do they do (to our spectra)
  • How can we manipulate them
  • Oriented samples
  • Magic angle spinning
  • How can we exploit them
  • Cross polarization
  • Dipolar recoupling
  • How can we use them to probe structure/dynamics
    (2nd series of lectures)

4
Outline (1)
  • What is anisotropy
  • How does it effect NMR spectra
  • What interactions give rise to anisotropic
    properties?
  • Describing interactions tensors
  • Chemical Shielding Anisotropy
  • Orientational dependence of resonance frequency
  • Powder spectra
  • Dipolar interactions
  • Quadrupolar interactions

5
What is anisotropy
  • Something whose properties depend on its
    orientation
  • e.g. stress

6
How does it effect the NMR spectrum
  • Each molecular orientation gives rise to a
    difference resonance frequency
  • In powder we have the sum of all distributions
  • In the liquid state these anisotropic properties
    are averaged on the NMR timescale

7
Which interactions in NMR
Isotropic
Anisotropic
8
Describing interactions tensors (1)
  • We are concerned with 3 flavours
  • Zero rank tensors
  • Physical property independent of coordinate
    system in which it is described (scalar,
    distance)
  • First rank tensors
  • Coordinate, depends on frame of reference
    (vector, has size and direction)
  • Second rank tensors
  • Multiple first rank tensors e.g. stress (matrix)
  • Higher rank exist but we will not be considering

9
Describing interactions tensors (2)
  • Rank zero tensor
  • Rank one tensor

B0
Isotropic chemical shift, J-coupling
(0,0,Bz)
10
Describing interactions tensors (3)
  • Second rank tensors

11
Parameterizing 2nd rank tensors
  • In cartesian notation tensors defined by
    principle components, Axx, Ayy andAzz
  • Frequently parameterized with
  • This assumes
  • Thus the asymmetry 0.0lt?lt1.0 and anisotropy can
    be both positive and negative

12
Chemical Shielding Anisotropy (1)
  • Perturbation of the magnetic field due to
    interaction with surrounding electrons
  • Inherently asymmetric (e.g. electron distribution
    surrounding carbonyl group)

13
Chemical Shielding Anisotropy (2)
  • We can describe the perturbation of the main
    field (B0), by the second rank tensor, s.
  • The Hamiltonian which describes the interaction
    with the modified field is
  • Which can be written in a simplified form as

14
Chemical Shielding Anisotropy (3)
  • Thus the chemical shielding Hamiltonian
    simplifies to
  • and the resonance frequency of the line is
  • Thus the resonance frequency is proportional to
    szz in the laboratory frame.
  • However, s is usually defined in the principle
    axis system (PAS) not in the lab frame (LF).
    Therefore, we need to transform s from the PAS to
    LF.

15
Transformations
Principle Axis System
Lab Frame
  • Rotation characterized by the three Euler angles
    (a, b and g)
  • Multiple s by rotation matrix R

16
Transformation matrix
  • Can derive a rotation matrix which bring about
    the rotation described above
  • To determine s in the laboratory frame, need to
    apply to the chemical shielding tensor s in the
    principle axis system
  • This can be simplified to give general
    Hamiltonian for CSA in lab frame of

17
Effect on resonance position
d/2
d
  • siso 1/3(sxxsyyszz) 0Hz
  • szz-siso 3000 Hz
  • h (syy-sxx)/d 0.0

18
Powder Patterns
  • In powders we have a random distribution of
    molecular orientations.
  • Thus the lineshape is the weighted superposition
    of all the different orientations

19
Empirical relation between PAS and MF
  1. Methyl carbons ? axially symmetric, axis along
    threefold symmetry axis
  2. Ring carbons ? three distinct tensor elements,
    most shielded perpendicular to plane, least
    shielded bisecting C-C-C angle of ring
  3. Most shielded direction
  4. Perpendicular to ring in aromatic carbons
  5. Along C3 axis for methyl carbons
  6. Perpendicular to the sp2 plane for
    carbonyl/carboxylic acids
  7. Least shielded direction
  8. In the ring plane, bisecting C-C-C angle
  9. Perpendicular to C3 axis for methyl groups
  10. In the sp2 place for carbonyl/carboxylic acids
  11. Intermediate shielding
  12. Tangential to ring for aromatic systems
  13. In the sp2 plane and perpendicular to the C-C
    bond for COOH

20
Dipolar Interaction
  • Classical interpretation
  • Classical interaction energy between two magnetic
    (dipole) moments when both are aligned with the
    magnetic field
  • Quantum mechanical
  • where
  • Symmetric second rank axially symmetric tensor.
  • Again we need to rotate from the PAS to LF to
    obtain resonance frequency.

21
Orientation dependence of dipolar interaction
  • Homo-nuclear Dipolar Hamiltonian
  • Hetero-nuclear Dipolar Hamiltonian

1/2ddip
3/4ddip
ddip20 kHz
22
Quadrupolar Interaction (1)
  • If spingt1/2, nucleus contains an electronic
    quadrupole moment (Q).
  • Electronic quadrupole moment interacts with
    surrounding electron cloud (electric field
    gradient(EFG), V).
  • where
  • Again we can define the anisotropy and asymmetry

23
Quadrupolar Interaction (2)
  • To calculate the resonance frequency, we must
    transform from the PAS of the EFG to the
    laboratory frame.
  • Retaining only the secular terms gives the
    following Hamiltonian in the LF

Powder spectrum of Ala-d3
dQ
Orientation dependence of a single crystal of
Ala-d3
24
Exploitation of anisotropic interaction
  • Oriented samples
  • Single Crystal studies
  • Oriented Biological Membranes
  • Dynamics
  • Averaging of anisotropic interaction
  • Local electronic environment
  • Perturbation in chemical shielding anisotropy

25
Dynamics averaging of anisotropy
Axis of rotational averaging
Gel Phase
q
Liquid Crystalline Phase
26
Oriented samples
  • Necessary to introduce macroscopic alignment
  • Crystallization
  • Oriented membranes
  • Fibres (Silk/DNA)

27
Oriented samples ligand orientations
B0
B0
28
Protein Backbone Orientation
15N chemical shielding anisotropy
Bo
Opella et al. 1998
15N-1H hetero-nuclear dipolar coupling
29
Local electronic environment
HCl
As we shall see next week, typically these
parameters are obtained under conditions of
magic-angle spinning to enhance signal to noise.
30
An aside spherical tensors
  • Make the calculations a lot easier to handle
  • Frequently used in papers

31
Change of time
  • Unable to make next weeks seminar
  • Propose to move to 10 February have one 2 hour
    solid-state 1st hour, liquid state 2nd hour.
  • Workshop scheduled for this Friday, move to the
    6th February.

32
Sensitivity and resolution enhancement in
solid-state NMR
33
Resume
Isotropic
Anisotropic
34
Oriented samples
  • Increase resolution by orienting interactions,
    therefore all spins resonate at the same
    frequency
  • As all spins resonate with the same frequency the
    sensitivity of the measurements is higher

35
Magic-angle spinning
36
Magic Angle Spinning
  • Seeks to reintroduce averaging process through
    mechanical rotation

Sample rotors (Varian)
Magic Angle Spinning Probehead (Doty)
37
Averaging of anisotropic interactions
38
Averaging of anisotropic interactions
  • The Hamiltonian becomes time dependent
  • We can deconvolute this into the iso- and
    an-isotropic contributions
  • where
  • and
  • Where C1, C2, S1 and S2 relate the anisotropic
    interaction to magnetic field (Appendix 1).

39
Analysis of MAS spectra
  • All anisotropic interactions become time
    dependent
  • To analyze spectra need to treat these time
    dependencies
  • Several mathematical descriptions that allow us
    to do this
  • Average Hamiltonian Treatment
  • Floquet Theory
  • Piece wise integration

40
Slow speed spinning
  • Rotational echoes apparent in fid which
    characterise the anisotropy of the interaction
  • At lower spinning speed the intensity of the
    sidebands characterises the anisotropic
    interaction (d and h)
  • 2ns

41
Herzfeld-Berger Analysis
  • Expression exist to calculate the intensity of
    sidebands for a given anisotropic interaction
  • where
  • and

1) Herzfeld and Berger, J.Chem.Phys 73 (1980) 6021
42
CSA analysis in reality
  • Several programs now available that now
    facilitate this task
  • Tables Paper by Herzfeld and Berger
  • matNMR (routines for analysis of both CSA and
    quadrupolar interactions in bothe static and MAS
    spectra) http//matnmr.sourceforge.net/ (requires
    matlab)
  • MAS sideband analysis (Levitt group homepage)
    http//www.mhl.soton.ac.uk/public/Main/index.html
    (requires mathematica)

43
Effect of off-angle MAS
  • Anisotropic interaction scaled by ½(3cos2q-1)
  • Useful for characterizing anisotropy whilst
    gaining some sensitivity
  • Indicates why magic angle should be carefully set!

44
When does MAS not work?
  • Homogeneous interactions
  • e.g. Homonuclear dipolar interactions
  • Heterogeneous line-broadening
  • e.g. Samples with conformational heterogeneity
    (lyophilized solids)
  • Nuclei with large quadrupolar interactions
  • When samples are not solid

45
Applications of MAS
  • Resolution/Sensitivity Enhancement?
  • Low speed spinning characterisation of
    anisotropy

Isotropic chemical shifts in the protein backbone
are sensitive to secondary structure Analysis of
the principle components of the chemical
shielding tensor reveals that larger changes are
seen in s22 making it a sensitive probe of
protein secondary structure.
Wei et al. 2001 JACS 123 6118-26
46
Applications of MAS
  • Low speed spinning
  • anisotropy?mobility
  • Amyloid precursor protein in differing lipid
    environments has different propensity to
    oligomerise. Sideband analysis reveals changes in
    peptide mobility
  • Marenchino et al. Biophysical Journal 2008

47
Cross Polarization
48
Why dont we normally detect protons in the
solid-state
  • Strong couplings between protons (dIIgt20kHz)
  • Homogeneous interaction
  • Not readily averaged at moderate spinning speeds
  • Methods for removing the couplings between
    protons during acquisition challenging
  • Result
  • Typically we exploit low-g nuclei

BPTI
Rhodopsin
49
Disadvantages of detecting low-g nuclei
  • Natural abundance levels not always high
  • enrichment
  • Low gyromagnetic ratio means the signal is
    attenuated
  • Solution transfer of polarization from protons to
    low g-nuclei (INEPT?)

50
1D 1H/15N INEPT NMR Spectrum
QUESTION What form does the 15N signal take?
51
Why is INEPT not typically used in the
solid-state?
  • J-couplings exist in the solid-state why not use
    them
  • Inhomogeneous broadening, short T2 reduce
    sensitivity
  • Could use re-focussed INEPT by T2 problems still
    attenuate signal

52
Cross-polarisation
  • In solid-state NMR we have other interactions we
    can exploit.
  • Strong coupling between a bath of 1H and low g
    nuclei.

53
Outline of what is happening
  • Transfer of polarization from 1H to low-g nuclei

(Spin Lock)x
(p/2)y
1H
(Spin Lock)x
X
54
How does the transfer occur
  • Several models the explain behaviour
  • Quantum mechanical
  • Coherent description of transfer of magnetization
    between two spins.
  • Thermodynamic
  • Coupling of a high temperature bath (proton,
    abundant magnetization) with a low temperature
    both (low-g nuclei) via the dipolar coupling and
    the equilibration of temperature.
  • 3) Ingenious?

55
Hahns Ingenious Concept1 (1)
  • Normally two heteronuclear spins resonate at
  • wIgIB0 and wSgSB0
  • and pulses applied to I or S affect I or S.
  • If we apply resonant fields to I and S they
    precess with a frequency
  • WIgIB1I and WSgSB1S
  • We can make the precession frequencies match by
    adjusting the frequency B1 of individual nuclei.
    When these conditions match we obtain the so
    called Hartmann-Hahn condition
  • gIB1I gSB1S

1) Principles of magnetic resonance, C.P.
Slichter p277
56
Hahns Ingenious Concept1 (2)
  • Fulfilled Hartmann-Hahn condition
  • gIB1I gSB1S
  • I spin in close proximity to S spin so we have a
    strong heteronuclear dipolar coupling
  • Thus we can get resonant transfer of energy from
    the I to the S spin.

1) Principles of magnetic resonance, C.P.
Slichter p277
57
Experimentally what is observed(1)
  • The width of the matching condition is
    proportional to the strength of the dipolar
    coupling in both the static and MAS
    cross-polarisation experiment.

58
Experimentally what is observed(2)
  • For a single coupling between I and S build-up is
    osscilatory
  • MS1/2(1-cos(wISt))
  • However wIS is orientation dependent and the
    efficiency is governed by the powder
    distribution. Result maximum efficiency is 72
  • In reality many protons are coupled to a given
    low-g nuclei and the build-up is not oscillatory
    and behaviour can be described as an exponential
    build-up.

59
Hartmann-Hahn Condition under MAS
  • Under MAS the heteronuclear dipolar coupling is
    averaged, cross polarisation shouldnt work!
  • As shown by Stejskal and Schaeffer transfer does
    occur as coupling is not completely averaged but
    becomes time dependent.
  • Under these conditions the Hartmann-Hahn
    condition breaks down into
  • gIB1I gSB1Sn
  • where n1,2 (at longer mixing times n0 is also
    visible)

Matching Condition for adamantane with a
contact Time of 1 and 16ms respectively with 5
kHz MAS
60
Effects of dynamics on cross polarisation
Buildup of magnetization dependent on
dynamics THC ? ms timescale T1r ? ms
timescale Profiles can be used to analyze
dynamics and follow the following behavior
Increasing T1r
61
Advantages of cross-polarisation
  • The low-g polarization is enhanced by gI/gS
  • e.g. for 15N gI/gS10, for 13C gI/gS4
  • As the polarization is derived from the protons,
    which typically relax faster than low-g nuclei
    the recycle delay of the experiment can typically
    be faster

62
Experimental difficulties applying CP
  • In both static and MAS cross polarisation the
    width of the matching condition is proportional
    to the strength of the heteronuclear dipolar
    coupling.
  • For weak couplings or mobile samples (where the
    dipolar coupling is averaged) width is small and
    experimentally it is difficult to match the
    Hartmann-Hahn condition
  • Small fluctuations in amplifier output can cause
    a miss-setting of the Hartmann-Hahn condition
  • Distribution of rf fields within the sample coil

63
Improvements on the basic idea
  • Ramped cross polarization
  • Adiabatic cross polarization (100 transfer?)
  • Multitude of others in literature.....

64
Application of CP
  • Signal enhancement?
  • Motional Filter
  • Characterising Motions
  • THC/T1r?
  • SHC

65
Application of CP
66
Coherent build-up of CP ? Dynamics
Coherent build-up of intensity enables the
strength of the dipolar coupling between the 1H
and 13C to be determined. This can be used to
determine an order parameter/measure of mobility
for individual sites within the protein. Lorieau
and McDermott (2006) JACS 12811505-12
67
Solid-state NMR spectra
68
References
  • Spin Dynamics Basics of Nuclear Magnetic
    Resonance, Malcolm Levitt
  • Biomolecular NMR, Jeremy Evans
  • Principles of Magnetic Resonance, C.P. Slichter

69
Appendix 1
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