Biochemistry 530

NMR Theory and Practice

Gabriele Varani

Department of Biochemistry

and

Department of Chemistry

University of Washington

Lecturer: Gabriele Varani

Biochemistry and Chemistry

Room J479 and Bagley 63

Phone: 543 7113

Email: varani@chem.washington.edu

Office Hours by arrangement

Lecture 1: Basic Principles of NMR

Lecture 2: 2D NMR

Lecture 3: NMR assignments/structure determination

Lecture 4: 2D and 3D heteronuclear NMR

Recommended NMR Textbooks

Derome, A. E. (1987)

Modern NMR Techniques for Chemistry Research, Pergamon Press

Wüthrich, K. (1986)

NMR of Proteins and Nucleic Acids , John Wiley and Sons

Roberts, G. C. K. (1993)

NMR of Macromolecules: A Practical Approach, Oxford Univ. Press

Cavanagh, J., et al. (1996)

Protein NMR Spectroscopy, Principles and Practice, Academic Press

Evans, J. N. S. (1999)

Biomolecular NMR Spectroscopy, Oxford Univ. Press

Useful websites

http://www.ch.ic.ac.uk/local/organic/nmr.html

NMR Spectroscopy. Principles and Application.

Six second year lectures given at Imperial College, U.K.

http://uic.unl.edu/nmr_theory.html

http://www.shu.ac.uk/schools/sci/chem/tutorials/molspec/nmr1.ht

m

Theoretical principles of NMR

Courtesy of Sheffield Hallam University, U.K.

http://www.nature.com/nsb/wilma/v4n10.875828203.html

links to various NMR and structural biology web sites

simulation and analysis software; NMR research groups, etc.

http://www.ch.ic.ac.uk/local/organic/nmr.html

NMR Spectroscopy. Principles and Application.

Six second year lectures given at Imperial College, U.K.

http://uic.unl.edu/nmr_theory.html

http://www.shu.ac.uk/schools/sci/chem/tutorials/molspec/n

mr1.htm

Theoretical principles of NMR

Courtesy of Sheffield Hallam University, U.K.

http://www.nature.com/nsb/wilma/v4n10.875828203.html

links to various NMR and structural biology web sites

simulation and analysis software; NMR research groups,

etc.

NMR spectrum of a protein: hundreds of

individual resonances resolved

1D spectrum

amides Ha Side chain CH2

Side chain CH3

NH2

Fourier-transform NMR (Ernst, 1965)

Signal - FID

(time domain)

Spectrum

(frequency domain)

2D NMR spectrum of a protein

2D projection

representation

2D contour

representation

RRM1 RRM2

ω2(1HMethyl) [ppm]

1(1

3C

Met

hyl )

[p

pm

]

13C methyl HMQC on selectively labeled protein

ω2(1HMethyl) [ppm]

1(1

3C

Met

hyl )

[p

pm

]

RRM1 RRM2

13C methyl HMQC on protein-RNA complex

ω2(1HMethyl) [ppm]

1(1

3C

Met

hyl )

[p

pm

]

Rna14

RRM1 RRM2 Rna15

L205d2

L274d1

V300g2

V247g2

V297g2

V185g2

I313d1 I228d1

I222d1

V217g1

V175g2

13C methyl HMQC on 300 kDa complex

Rna15

Hrp1

RNA

Rna14

180

Define and identify protein interaction sites in

large complexes

50100150200250

50

100

150

200

250

162

156

158

160

164 14 13 12 11

U68

U16,U70

U17

U71

U82

U28

U68

U16,U70

U17

U82

U40

U71

U41

U22

U77

U34

U25

U74

U49

U47

U39

U31

Standard (10 min)

50100150200250

50

100

150

200

250

162

156

158

160

164

14 13 12 11

Ultrafast NMR (2-3s)

Ultrafast acquisition of NMR spectra

Bound riboswitch

1212.212.412.612.81313.213.413.6

144

145

146

147

148

149

150

151

13 12

150

144

146

148

t = 0 sec

G81 G59

G43 G44

G57

G14

G78 G72

Conformation changes in real time

1212.212.412.612.81313.213.413.6

144

145

146

147

148

149

150

151t = 16 sec

G14

G78

G57

G81

G59

G43

G44

Conformation changes in real time

1212.212.412.612.81313.213.413.6

144

145

146

147

148

149

150

151t = 28 sec

G14

G78

G44

G57

G43

G38,G59

G32

G81

G37

G46

Conformation changes in real time

1212.212.412.612.81313.213.413.6

144

145

146

147

148

149

150

151

t = 58 sec

G14

G78

G43

G44 G57

G38,G59

G37

G32

G81

Conformation changes in real time

The Spectrometer: 1. A powerful magnet

AD

C

PRE-AMPRECEIVER DETECTOR

TRANSMITTER

CONTINUOUS REFERENCE

BINARY NUMBERS TO COMPUTERS

= 500 MHz = 500,000,000 Hz

499,995,000 < o < 500,005,000 Hz

sample

PROBE

Magnet

+-

+-5,000 Hzo- =

The Spectrometer: 2 A Radio station

• The transmitter generates short (<0.1 ms) RF pulses to the probe

• RF pulses stimulate nuclear spin transitions in the sample

• The emitted signal is measured by the receiver and digitized

• RF signals arising from the sample are all in the region of

500 MHz, differing only by the chemical shift range present

AD

C

PRE-AMPRECEIVER DETECTOR

TRANSMITTER

CONTINUOUS REFERENCE

BINARY NUMBERS TO COMPUTERS

= 500 MHz = 500,000,000 Hz

499,995,000 < o < 500,005,000 Hz

sample

PROBE

Magnet

+-

+-5,000 Hzo- =

For protons this is typically 10

ppm or 5000 Hz at 500 Mhz

If we subtract some reference

frequency ( = 500 MHz)

from the signal, we only digitize

the chemical shifts (o-)

(audiofrequencies)

Spectrometer performance: sensitivity and

stability

AD

C

PRE-AMPRECEIVER DETECTOR

TRANSMITTER

CONTINUOUS REFERENCE

BINARY NUMBERS TO COMPUTERS

= 500 MHz = 500,000,000 Hz

499,995,000 < o < 500,005,000 Hz

sample

PROBE

Magnet

+-

+-5,000 Hzo- =

• The probe is in many ways

the ‘heart’ of the spectrometer:

it determines s/n (e.g.

cryoprobes)

• Magnet homogeneity and

long term stability determine

resolution (1 part in 109)

• Stability of RF

amplifier/signal pre-

amplifier/frequency generation

units determine artifacts (1

part in 109)

Spectrometer performance: Magnetic field

strength provides increased resolution

500 Mhz (1 peak?)

750 Mhz (2 peaks?)

800 Mhz (2 peaks!)

The chemical shift scale

The frequency of absorption of the NMR signal depends on the

external field as we have seen

n0 = g B0/2p

Let us now introduce a quantity that describes the fact that

different nuclei in the sample experience slightly different

magnetic fields because of chemical structure and

conformation

n = (1-s) g B0

Finally, let us introduce a scale that is field-independent, so that we

can compare directly data recorded on different spectrometers:

d=(n-no)/n0x106

We use a standard sample (e.g. DSS) to reference all of our

spectra, so that we can report the resonance frequency for our

proton in a universal, field-independent manner

The NMR Signal and Spectrum

Signal - FID

(time domain)

Spectrum

(frequency domain)

The NMR Signal and Spectrum

• The emission signals are oscillatory and physically damped

(damped harmonic oscillations)

• This signal is called the Free Induction Decay or FID

• The actual spectrum is recovered from the FID via Fourier

transformation, which transforms the time interferogram into a

frequency spectrum

• Without FT NMR, it would take the square of the time to obtain an

equivalent signal/noise ration

Example: FID and a 1D spectrum

1D

spectrum

FID

Fourier Transform

Origin of the NMR signal

Nuclear subatomic particles have spin

1. If the number of neutrons and protons are both even

the nucleus has 0 spin

i.e. 12C (6 neutrons + 6 protons = 12) has I = Ø spin

2. If the number of neutrons plus protons is odd

the nucleus has a half-integer spin (1/2, 3/2, 5/2)

i.e. 13C (7 neutrons + 6 protons = 13) has I = 1/2 spin

3. If the number of neutrons and protons are both odd

then the nucleus has an integer spin (1, 2, 3)

i.e. 14N (7 neutrons + 7 protons = 14) has I = 1 spin; spin 1

nuclei are quadrupolar (relax fast)

For high resolution applications, we use spin ½ nuclei (1H, 13C, 15N, 31P in biology);

Nuclear spins and the energy levels in a magnetic

field

• A nucleus of spin I has 2I + 1 possible orientations

(a nucleus with spin 1/2 has 2 possible orientations)

• Each level is given a magnetic quantum number m

• The energy levels for a 1H nucleus are referred to as:

a (m = +1/2) and b (m = -1/2)

In the absence of an external magnetic field, these orientations have

equal energy; if a magnetic field is applied, energy levels are split

The a state is the energetically preferred orientation

(magnetic moment parallel with the applied magnetic field)

The b state has higher energy

(magnetic moment anti-parallel to the applied magnetic field)

Nuclear spins and the energy levels in a magnetic

field

The energy of a particular level is given by:

E = g h m Bo

where: g is the the gyromagnetic ratio, a nuclear property

(a measure of the polarizability of the nucleus)

h is Planck's constant divided by 2p (h = h/2p )

Bo is the strength of the magnetic field

The difference in energy between levels (the transition energy)

DE = g h Bo

If the magnetic field is increased, so is DE

(as DE increases, so does sensitivity)

NMR properties of nuclei of common use in

biology

Isotope Spin Abundance Magnetogyric ratio NMR frequency

(I) g/107 rad T-1s-1 MHz (2.3 T magnet)

1H 1/2 99.985 % 26.7519 100.000000 2H 1 0.015 4.1066 15.351 13C 1/2 1.108 6.7283 25.145 14N 1 99.63 1.9338 7.228 15N 1/2 0.37 -2.712 10.136783 17O 5/2 0.037 -3.6279 13.561 19F 1/2 100 25.181 94.094003 23Na 3/2 100 7.08013 26.466 31P 1/2 100 10.841 40.480737 113Cd 1/2 12.26 -5.9550 22.193173

Nuclear precession in a magnetic field: semi-

classical description

y

Bo

x

z The nucleus has a positive charge

and spins

This generates a small magnetic

field

The nucleus possesses a magnetic

moment m proportional to its spin I

• In a magnetic field, the axis of rotation will precess about

the magnetic field Bo

• The frequency of precession (o Larmor frequency)

is identical to the transition frequency (o = -gBo)

• The precession may be clockwise or anticlockwise

depending on the sign of the gyromagnetic ratio (+g or -g)

Origin of a macroscopic (observable) NMR signal

Out of a large collection of

moments, a surplus have

their z component aligned

with the applied field, so

the sample becomes

magnetized in the direction

of the main field Bo

• The parallel orientation is of lower energy than the antiparallel

• At equilibrium, spins will be distributed according to Boltzmann

distribution between the two energy states

• A net magnetization parallel to the applied magnetic field arises

because of the small population difference between states

z

Bo

y

x

Mo

Sensitivity of NMR experiment

Nuclei populate energy levels according to Boltzmann distribution

n1/n2 = exp (-DE/kT)

If we irradiate the system on resonance (DE=hn), the probability of

signal absorption will be proportional to the population

difference:

n2-n1

If DE>>kT (e.g. optical spectroscopy) then all dipoles are in the

ground state

If DE<kT (NMR), then the net absorption of energy will be small

because n2=n1 and stimulated emission/absorption are equally

probable

The only thing you can do is increase the magnetic field,

because

DE = g h Bo

S/N in NMR is poor because energy levels are so

close

According to Boltzmann’ distribution:

kTEEe

n

n /)(

2

1 21

If the system is exposed to a frequency: h

EEv 12

then the energy absorbed is proportional to the difference

(as is the case for optical spectroscopy), then essentially

all the molecules will be in their ground state configuration

if kTE D 12 nn

S/N in NMR is poor because energy levels are so

close

kTEEe

n

n /)(

2

1 21

(as is the case for NMR spectroscopy), then the net

absorption of energy will be very small because the rate of

upward transitions is equal to the rate of downward

transitions

For this reason, we use magnets of increasing strength to

separate energy level more and increase the sensitivity of

the experiment

If instead kTE D21 nn