NMR Spectroscopy

Basic NMR theory

Lecture 1

Jamil Saad

Useful Literature

1)  High-Resolution NMR Techniques in Organic Chemistry. By Timothy D.W. Claridge, Elsevier Science; 1st edition (1999).

2)  Nuclear Magnetic Resonance. By P.J. Hore, Oxford University Press, USA; 1st edition (1995).

3)  Basic One- and Two-Dimensional NMR Spectroscopy. By Horst Friebolin, Wiley-VCH; 4 edition (2005).

4)  Online NMR course: http://www.cis.rit.edu/htbooks/nmr/inside.htm 5)  NMRVIEW http://www.onemoonscientific.com/nmrview/ 6)  NMRPIPE “http://spin.niddk.nih.gov/NMRPipe/”

What is an atom?

  The smallest unit of an element.

  Has an electron cloud consisting of negatively charged electrons surrounding a dense nucleus.

  The nucleus contains positively charged protons and electrically neutral neutrons.

  When the number of protons in the nucleus equals the number of electrons, the atom is electrically neutral.

  Otherwise, it is an ion and has a net positive or negative charge.

  An atom is classified according to its number of protons and neutrons: the number of protons determines the “chemical element” and the number of neutrons determines the “isotope” of that element.

  The electrons determine the chemical properties of an element, and strongly influence an atom's magnetic properties.

What is nuclear magnetic resonance?

Nuclear perturbation Nuclear reaction

Structure/imaging from molecules to animals

10-3?

Applications

Medicine: Magnetic resonance imaging (MRI)

a brain tumor (meningioma)

A distinctive chemical which is generally only seen in meningiomas

Structural Biology: Proteins, DNA/RNA, Protein-DNA/RNA complexes, Protein-lipid complexes, and Polysaccharides

This is an example of the kind of biochemical information which can help doctors to make their diagnosis.

Chemistry: synthesis, pharmaceutical, quality control, structure, conformation, dynamics, kinetics, chemical exchange, equilibrium, molecular tumbling, etc…

Drug design: Structure Activity Relationships (SAR)

Petroleum industry: test water, oil, organic, inorganic composition.

Process control: mining, polymer production, cool analysis, cosmetics..

Food industry: drinks, solid foods, quality, contents, contamination..

Environmental: fertilizers, pesticides, pollution, heavy metals..

Natural product analysis: extracts, potential drug leads..

1946 Bloch, Purcell First nuclear magnetic resonance (30 MHz) 1955 Solomon NOE (nuclear Overhauser effect) 1966 Ernst, Anderson Fourier transform NMR 1975  Jeener, Ernst Two-dimensional NMR 1985 Kurt Wüthrich First solution structure of a small protein from NOE-derived

distance restraints

1987/8 3D NMR + 13C, 15N isotope labeling 1996/7 New long-range structural parameters:

- residual dipolar couplings (also: anisotropic diffusion) - cross-correlated relaxation TROSY (molecular weight > 100 kDa)

2003 First solid-state NMR structure of a small protein

Nobel prizes

1944 Physics: Rabi (Columbia) [resonance method for recording the magnetic properties of atomic nuclei] 1952 Physics: Bloch (Stanford), Purcell (Harvard) [First NMR] 1991 Chemistry: Ernst (ETH) [development of NMR methodology] 2002 Chemistry: Wüthrich (ETH) [first 3D structures by NMR] 2003 Medicine: Lauterbur (Urbana), Mansfield (Nottingham) [MRI]

History of NMR

Ethanol proton spectrum @700 MHz

First proton spectrum of ethanol @ 30 MHz

Details of the 20S proteasome structure: Quantification of dynamics and structure (670 kilodalton)

Nature 445, 618-622 (2007)

Why biomolecular NMR??

  Biological molecules such as proteins and nucleic acids can be large and complex. They can easily exceed 2000 atoms. Knowing their structure is critical in understanding the relationship between structure and function.

- no crystal needed, native-like conditions: solution, (in cell) NMR - many biological samples can be difficult to crystallize. e.g., nucleic acids

structures are affected by crystal packing

  NMR can be used to determine 3D structure and dynamics in solution! It’s limitation is molecular size. However, this is changing.

Molecular weight: X-ray: > 200 kDa, NMR < 50-100 kDa, 900 kDa!?

  Ligand binding and molecular interactions in solution

  Characterization of dynamics and mobility (ps - days) - conformational dynamics, enzyme turnover, kinetics, folding

Structure determination by NMR

4D ???

A conceptual block diagram of the FT NMR

•  Spectroscopy is the study of the interactions between light and matter as a function of wavelength (λ).

•  Light refers to any sort of electromagnetic radiation, such as visible light, UV, IR, and radiowaves.

•  Depending on the frequency or wavelength of the radiation involved we will have different types of interactions with matter (molecules).

10-10 10-8 10-6 10-4 10-2 100 102

wavelength (λ, cm)

γ-rays x-rays UV VIS IR µ-wave radio

wavelength and frequency are inversely proportional, so higher frequencies mean shorter wavelength.

•  The relationship between energy and frequency:

h = Plank’s constant υ = frequency

ΔE = hυ

•  The higher the frequency, the higher the energy. In addition, depending on the frequency and wavelength we’ll have different interactions with matter (molecules).

E, υ

λ

•  Detects the absorption of radiofrequencies (electromagnetic radiation) by certain nuclei in a molecule.

•  The nuclei of all atoms may be characterized by: a nuclear spin quantum number (I)

•  Only nuclei with spin number (I) ≠ 0 can absorb/emit electromagnetic radiation. These have an odd mass #.

Mass # Atomic # I Example

Odd Even or odd 1/2, 3/2, 5/2,… (1H, 13C, 15N, 31P) Even Even 0 (12C, 16O) Even Odd 1, 2, 3 (14N, 2H)

Nuclear magnetic resonance (NMR) is a physical phenomenon based upon the quantum mechanical magnetic properties of an atom's nucleus.

µ = γ P

•  γ is the gyromagnetic ratio, and it depends on the nature of each nuclei (constant for any given nuclei).

The spinning nuclei possess angular momentum (P). Charge and motion of this charge gives rise to magnetic moment (µ)

µ

•  Different nuclei have different magnetic moments.

Vector quantities: They both have magnitude and direction

The spin states of the nucleus (m) are quantized: magnetic quantum number (m) = I, (I - 1), (I - 2), … , -I

For 1H, 13C, 15N, 31P (biologically relevant nuclei with I = 1/2):

m = 1/2, -1/2 This means that only two states (energy levels) can be taken by these nuclei.

•  For a particular nuclei, the magnetic moment (µ):

µ = γ I h / 2π

•  The energy of a spin in a magnetic field (E) will depend on a static magnetic field called Bo, and µ.

E = - µ . Bo

Bo Tesla (T)

•  When the Bo field is applied, spins have two possible energy limits (1/2, -1/2). In one we are in favor of the field, and in the other one we are against it:

Bo µ Bo µ

Eα = - γ h Bo / 4π

•  The larger the Bo, the larger the energy difference.

•  The energy difference of the two levels, α and β, is:

E = - µ . Bo

ΔE = γ h Bo / 2π

Eβ = γ h Bo / 4π

•  ΔE for 1H’s at Bo = 9.4 T is 4 x 10-5 Kcal / mol.

Magnetic energy and populations

m = 1/2

m = -1/2

ΔE2 ΔE1

B B1 B2

KB = Boltzman constant = 1.3805x10-23 JK-1

At equilibrium, there is excess of nuclei in the a state:

The population ratio between the two levels depends on ΔE, and we can apply a Boltzmman distribution.

Bo E Quantum Mechanical Description

Nα / Nβ = e ΔE/KBT

Nβ / Nα = e -ΔE/KBT

Since ΔE is very small compared with the average energy of KBT thermal motion:

Nβ / Nα = 1-ΔE/KBT = 1-(γ h Bo / 2πKBT)

Nuclei with larger γ will absorb/emit more energy, and will therefore be more sensitive. Sensitivity is proportional to µ and Nα / Nβ

γ (13C) = 6,728 rad / G

γ (1H) = 26,753 rad / G •  1H is ~ 64 times more sensitive than 13C only due to γ.

•  If we also take into account the natural abundance, 13C (1.1%) ends up being 6400 less sensitive than 1H.

•  Nα / Nβ ratio is only 1.000064. Calculate!

•  In 1000,000 spins, difference is just 64: NMR is very insensitive when compared to UV or IR.

•  We call this Larmor precession (named after Joseph Larmor) or angular frequency, ωo (radians) or ν (Hz):

ωo = - γ Bo (rad s-1)

•  In the presence of a magnetic field two forces act on the spins: One that tries to align them with Bo, while the other tries to maintain their angular momentum. • The net result is that the nuclei spins trace a circular path about the applied field.

Bo ν = - γ Bo / 2π (Hz) Larmor Frequency

ω

µ

µ

ω

•  There are several magnetic fields acting on the spins. One is Bo, which is constant and generates the precession at ωo. The others are fluctuating due to the molecular anisotropy and its environment, and make the spins ‘try’ all the possible orientations with respect to Bo in a certain amount of time.

•  Orientations in favor of Bo will have lower magnetic energy, and will be slightly favored. After a certain time, a net magnetization (Mo) pointing in the direction of Bo will develop.

ω z

x

ω

one nucleus

z

x y

ω

many nuclei

z

x

y

Mo - net magnetization vector allows us to look at system as a whole

The net magnetization vector

Mo

•  Where does the net magnetization come from? In order to figure it out we translate all the spins to the origin of the coordinate system. We’ll see something like this:

x

y

z

Bo

•  We’ll have a slight excess of spins aligned with Bo, but at any angle with respect to Z. The distribution is proportional to Nα / Nβ.

•  If we break down the µ vectors in Z and <xy>, we get:

Mo z

y

x Bo

y

y

=

= “0”

z z

•  The net magnetization is aligned with Bo, and this is what we use in NMR.

E = h νo νo = γ Bo / 2π ΔE = h νo = γ h Bo / 2π

  Nuclear magnetic resonance occurs when the nucleus changes its spin state from α to β.   This is driven by the absorption of a quantum of energy.   Coming from electromagnetic radiation, whose frequency must match that of Larmor precession:

Bo = 0 Randomly oriented Bo > 0

Highly oriented

Bo

N

S

Each nucleus behaves like a bar magnet.

•  So far nothing happened. We have a tube spinning in the magnet. To see something we have to move the system away from equilibrium. That is, we have to perturb its populations.

•  We need the system to absorb energy. That energy will induce transitions between energy levels that is to cause magnetic resonance to occur. The energy source is an oscillating electromagnetic radiation generated by an alternating current.

Mo

z

y

B1 = C * cos (ωot)

B1

Transmitter coil (provides rf pulse)

x Bo