NMR: Nucelar Magnetic Resonance Mikls Nyitrai, April 6, 2016 - - PDF document

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NMR: Nucelar Magnetic Resonance Mikls Nyitrai, April 6, 2016 - - PDF document

4/11/2016 What is the medical importance of NMR? (see lecture No. 13. in this semeter!) UNIVERSITY OF PCS MEDICAL SCHOOL www.medschool.pte.hu NMR: Nucelar Magnetic Resonance Mikls Nyitrai, April 6, 2016 www.medschool.pte.hu Physical


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UNIVERSITY OF PÉCS MEDICAL SCHOOL www.medschool.pte.hu

NMR: Nucelar Magnetic Resonance

Miklós Nyitrai, April 6, 2016

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What is the medical importance of NMR?

(see lecture No. 13. in this semeter!)

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Physical bases, spins and nuclei

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Protons and neutrons (and also the electrons) are particles having a spin angular momentum of 1/2. If the number of protons or neutrons is add in the nucleus, then the total nuclear spin will not be zero!

Spins and nuclei

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Properties of nuclear spin

Nucleus: proton and neutron Two magnetic moments (spin) pointing in opposite directions zero net magnetic moment! nuclei with even Z and even N have nuclear spin I=0 (isotopes are important) If there are unpaired protons or neutrons in a nucleus, then the net nuclear spin (the intrinsic nuclear magnetic momentum) differs from zero.

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Atoms for NMR

1H, 2H, 3H, 3He, 4He, 12C, 13C, 14C, 14N, 15N 16O, 17O, 19F, 23Na, 31P, etc.

The most frequently applied nuclei: 1H, 13C, 15N, 17O, 19F, F, 31P

Signal depends on:

  • Magnitude of the magnetic moment
  • Concentration of the isotope

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The split of the energy states (Zeemann)

N N S S

Spinning nucleus with it’s magnetic field alligned with the external field. Spinning nucleus with it’s magnetic field alligned against the external field. α-spin state, favourable, lower energy

N S N S

β-spin state, unfavourable, higher energy

The energy difference between the spin states does depend on the strength of the external magnetic field.

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m: magnetic moment of the individual atom

Orientation and reorientation on the microscopic level

µ µ H=0; M=0 µ µ µ H>0; M>0 M=Σµi

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Graphical representation

Remember, the energy is proportional to the frequency!

H E

at no magnetic field there is no difference between these states

α-spin state β-spin state

∆E1 ∆E2

<

H1 H2

<

N S N S S N N S www.medschool.pte.hu

An example: CH4

H E

α-spin state β-spin state

h x 300MHz

0 T 7,05 T 11,75 T

h x 500MHz We can probe the energy difference of the α - and β - state of the protons by irradiating them with EM radiation of just the right energy. In a magnet of 7.05 Tesla, it takes EM radiation of about 300 MHz (radio waves). So, if we bombard the molecule with 300 MHz radio waves, the protons will absorb that energy and we can measure that absorbance. In a magnet of 11.75 Tesla, it takes EM radiation of about 500 MHz (stronger magnet means greater energy difference between the α - and β - state of the protons).

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What is the problem with this concept?

It is difficult to compare the data from two instruments with different strenghts of magnetic fields.

Let’s use the chemical shift!

What is this? Much simpler than it may sound…

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Chemical shift or δ

We need a reference sample to standardize our insturments!

  • 1. Measure the absorbance frequency of the standard: fr;
  • 2. Measure the frequency for your own sample: fs;
  • 3. Let’s calculate the difference between the two: ∆f = fr - fs ;
  • 4. Normalise the difference with the ferquency of the reference: δ = ∆f / fr ;

The δ, i.e. the chemical shift will be characteristic for your sample, but will not depend on the parameters of the instrument used for the experiments!

Why? Let’s take an example!

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Imagine that we have a magnet where our standard absorbs at 300,000,000 Hz (300 megahertz), and our sample absorbs at 300,000,300 Hz. The difference is 300 Hz, so we take 300/300,000,000 = 1/1,000,000 and call that 1 part per million (or 1 PPM). Now lets examine the same sample in a stronger magnetic field where the reference comes at 450,000,000 Hz, or 450 megahertz. The frequency of our sample will increase proportionally, and will come at 450,000,450 Hz. The difference is now 450 Hz, but we divide by 450,000,000 (450/450,000,000 = 1/1,000,000, = 1 PPM).

(We do not have to calculate all these, the NMR machine does it for us!)

An example: chemical shift

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The absorption is proportional to the concentration of the corresponding nuclei. The NMR spectrum is the energy absorbed by the system as the function of the freqeuncy (f) of the excitation energy (ΔE) or the magnetic field (H, B). Due to local effects and fields the excitation energy (and thus frequency) is different for different nuclei.

NMR spectrum

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Structure of organic molecules and subtances; Interactions of organic molecules; Structure of macromolecules (proteins, nucleic acids); Biological and artificial membranes; MRI: Magnetic Resonance Imaging.

Applications of NMR

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SUMMARY

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Jablonski diagram

S0 S1 Ground-state S0 – S1 Excited-state Vibrational relaxation – heat (10-12s) excitation (10-15s) hν T1 T1 → S0 (10-3 – 10-1s ) vibrational levels

1 2 3 4 5

S1 → T1: inter- system crossing (10-10 – 10-8 s)

S1 → S0 (10-9s ) A → kt D

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substance

OD = A = - log (I / I0) = ε (λ) c x

I0 I

„optical density”

I = I0 10-ε(λ) c x

The definition of absoprtion

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light source sample detector monochromator

How to measure absorption?

A scheme of a photometer.

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The absorption of proteins

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The absorption of proteins

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Kasha’s-rule

The emission of the fluorescence light is allways starting from the lowes est vibrational level of the first excited level (S1).

Michael Kasha December 6, 1920 - June 12, 2013

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S T S S

In the ns range In the > ms range

Definition of fluorescence and phosphorescence

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Basic fluorescence parameters

Fluorescence spectrum, intensity; Quantum efficiency Fluorescence lifetime Polarisation

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Stokes-shift

The differ eren ence ce (measured in nm) between the peak of the excitation and the emission spectrum (energy loss).

fluorescence emission sp. fluorescence excitation sp. wavelength (nm)

Stokes

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Scheme of a spectrofluorometer

Non linear arrangement !!!

F M S M D

90o

light source excitation monochromator emission monochromator detection sample holder

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E r

Photoselection

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Scheme of a spectrofluorometer

F M S M D

90o

light source excitation monochromator emission monochromator detection sample holder

Polarisers in the light paths!!!

IVV IHV IVH IHH P P

Vertical or horizontal polarisers:

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Emission anisotropy

r = (IVV - GIVH) / (IVV + 2GIVH)

G = IHV / IHH

  • dimensionless
  • depends on rotational motion of the fluorophore
  • additive!

Vertica cally y align gned polar arizer er on the excitat ation side Horizo zontal ally align gned ed polar arizer er on the emission side

Isum = IZ + IX + IY Isum = IVV + IVH + IVH Isum = IVV + 2IVH Remember!

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Conditions of FRET

  • A fluores

escen cent donor molecule.

  • The appropriate orien

entat ation of the donor and

  • Over

verlap ap between the donor emission and acceptor absorption spectra.

  • Distance range of 2-10 nm!

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FRET efficiency

E = 1 – (FDA / FD)

where FDA: donor intensity with the acceptor FD : a donor intensity without the acceptor. Can also be calculated with lifetimes!

E = 1 – (τDA / τD)

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Distance dependence of the FRET efficiency

6 6 6

R R R E + =

Determination of distances! Molecular ruler!

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Applications of FRET

  • The determination of FRET distances

→ To study the establishment of interactions between molecules; → To study intra-molecular structural changes.

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Vibration modes of water molecules

http://www1.lsbu.ac.uk/water/vibrat.html www.medschool.pte.hu

spring = bond

Model for molecular vibrations

if matom ↑ then f ↓ (C-H: 3000 cm-1, C-Cl: 700 cm-1) if bond strength ↑ then f ↑ (C=H: 1650 cm-1, C≡C: 2200 cm-1)

mass = atom f ~ D / m

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Infra and Raman spectroscopy

IR abs. Rayleigh scatter Raman scatter S0 S1

Vibrational levels

hf0 h(f0-f1) h(f0+f1)

Vibrational levels

elastic

  • vs. non-elastic

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Example: regions of an IR spectrum

Double bonds (2000-1500) Triple bonds (2500-2000) ”Fingerprint” region (1500 - 600) Bonds to H (X–H) (4000-2500 cm-1)

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m: magnetic moment of the individual atom

Orientation and reorientation on the microscopic level

µ µ H=0; M=0 µ µ µ H>0; M>0 M=Σµi

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Graphical representation

Remember, the energy is proportional to the frequency!

H E

at no magnetic field there is no difference between these states

α-spin state β-spin state

∆E1 ∆E2

<

H1 H2

<

N S N S S N N S

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Chemical shift or δ

We need a reference sample to standardize our insturments!

  • 1. Measure the absorbance frequency of the standard: fr;
  • 2. Measure the frequency for your own sample: fs;
  • 3. Let’s calculate the difference between the two: ∆f = fr - fs ;
  • 4. Normalise the difference with the ferquency of the reference: δ = ∆f / fr ;

The δ, i.e. the chemical shift will be characteristic for your sample, but will not depend on the parameters of the instrument used for the experiments!

Why? Let’s take an example!

www.medschool.pte.hu

Structure of organic molecules and subtances; Interactions of organic molecules; Structure of macromolecules (proteins, nucleic acids); Biological and artificial membranes; MRI: Magnetic Resonance Imaging.

Applications of NMR

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Thank you!