Loading...

PPT – NMR (PG503) PowerPoint presentation | free to download - id: 46efb8-MTdhO

The Adobe Flash plugin is needed to view this content

NMR (PG503)

- Solid-state NMR Anisotropic interactions and how

we use them

Dr Philip Williamson February 2009

Solid-state NMR spectra

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)

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

What is anisotropy

- Something whose properties depend on its

orientation - e.g. stress

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

Which interactions in NMR

Isotropic

Anisotropic

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

Describing interactions tensors (2)

- Rank zero tensor

- Rank one tensor

B0

Isotropic chemical shift, J-coupling

(0,0,Bz)

Describing interactions tensors (3)

- Second rank tensors

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

Chemical Shielding Anisotropy (1)

- Perturbation of the magnetic field due to

interaction with surrounding electrons - Inherently asymmetric (e.g. electron distribution

surrounding carbonyl group)

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

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.

Transformations

Principle Axis System

Lab Frame

- Rotation characterized by the three Euler angles

(a, b and g) - Multiple s by rotation matrix R

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

Effect on resonance position

d/2

d

- siso 1/3(sxxsyyszz) 0Hz
- szz-siso 3000 Hz
- h (syy-sxx)/d 0.0

Powder Patterns

- In powders we have a random distribution of

molecular orientations. - Thus the lineshape is the weighted superposition

of all the different orientations

Empirical relation between PAS and MF

- Methyl carbons ? axially symmetric, axis along

threefold symmetry axis - Ring carbons ? three distinct tensor elements,

most shielded perpendicular to plane, least

shielded bisecting C-C-C angle of ring - Most shielded direction
- Perpendicular to ring in aromatic carbons
- Along C3 axis for methyl carbons
- Perpendicular to the sp2 plane for

carbonyl/carboxylic acids - Least shielded direction
- In the ring plane, bisecting C-C-C angle
- Perpendicular to C3 axis for methyl groups
- In the sp2 place for carbonyl/carboxylic acids
- Intermediate shielding
- Tangential to ring for aromatic systems
- In the sp2 plane and perpendicular to the C-C

bond for COOH

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.

Orientation dependence of dipolar interaction

- Homo-nuclear Dipolar Hamiltonian

- Hetero-nuclear Dipolar Hamiltonian

1/2ddip

3/4ddip

ddip20 kHz

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

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

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

Dynamics averaging of anisotropy

Axis of rotational averaging

Gel Phase

q

Liquid Crystalline Phase

Oriented samples

- Necessary to introduce macroscopic alignment
- Crystallization
- Oriented membranes
- Fibres (Silk/DNA)

Oriented samples ligand orientations

B0

B0

Protein Backbone Orientation

15N chemical shielding anisotropy

Bo

Opella et al. 1998

15N-1H hetero-nuclear dipolar coupling

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.

An aside spherical tensors

- Make the calculations a lot easier to handle
- Frequently used in papers

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.

Sensitivity and resolution enhancement in

solid-state NMR

Resume

Isotropic

Anisotropic

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

Magic-angle spinning

Magic Angle Spinning

- Seeks to reintroduce averaging process through

mechanical rotation

Sample rotors (Varian)

Magic Angle Spinning Probehead (Doty)

Averaging of anisotropic interactions

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).

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

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

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

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)

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!

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

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

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

Cross Polarization

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

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?)

1D 1H/15N INEPT NMR Spectrum

QUESTION What form does the 15N signal take?

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

Cross-polarisation

- In solid-state NMR we have other interactions we

can exploit. - Strong coupling between a bath of 1H and low g

nuclei.

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

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?

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

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

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.

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.

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

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

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

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

Improvements on the basic idea

- Ramped cross polarization
- Adiabatic cross polarization (100 transfer?)
- Multitude of others in literature.....

Application of CP

- Signal enhancement?
- Motional Filter
- Characterising Motions
- THC/T1r?
- SHC

Application of CP

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

Solid-state NMR spectra

References

- Spin Dynamics Basics of Nuclear Magnetic

Resonance, Malcolm Levitt - Biomolecular NMR, Jeremy Evans
- Principles of Magnetic Resonance, C.P. Slichter

Appendix 1