BSB 512 Nuclear Magnetic Resonance SpectroscopyTTh 2:20 - 3:25 pm

Lecture notes available at http://sos.bio.sunysb.edu/bsb512

Lecture 1: BasicsLecture 2-4: Protein structure determinationLecture 5: Relaxation and dynamicsLecture 6: Lab Session:

Sample preparation.Pulse ProgramsProbe selection.Tuning.ShimmingPulse calibration.Data collection.

References

http://www.cis.rit.edu/htbooks/nmr

Books

Wuthrich, K. NMR of Proteins and Nucleic AcidsLevitt, MH Spin DynamicsCavanagh J. et al. Protein NMR SpectroscopyErnst, R. et al. Principles of NMR in One and Two DimensionsBax, A Two dimensional NMR in Liquids

NMR Spectroscopy: Some history

1915 Einstein and de Hass - Correlation between magnetic moment and spin angular momentum

1922 Stern and Gerlach - Spins are quantized1946 Bloch and Purcell - First NMR experiment1967 Richard Ernst - Fourier transformations1971 Jean Jeener - Two dimensional NMR - COSY1976 Richard Ernst - First two dimensional NMR experiment1986 Kurt Wuthrich - First independent NMR - X-ray

comparison

High resolution solution NMRof proteins

• Observe protons (1H)

• This differs from x-raydiffraction where onedetermines structure basedon the electron density fromthe electron rich atoms(C, N, O).

• Protein is solubilized in water.

High resolution solution NMRof proteins

• Observe protons• Assign proton resonances to indivdual amino acids. Proton resonances are often resolved by differences in chemical shifts.• Measure intra-residue and inter-residue proton to proton distances through dipolar couplings.• Measure torsion angles through J-couplings.• Use distance and torsion angle constraints to determine secondary and tertiary structure.

High resolution solution NMRof proteins

• Protons have a property called spin angular momentum.

• They behave like small bar magnets and align with or against a magnetic field.

• These small magnets interact with each other.

Bo

S

N

S

N

13C and 15N also have spin angular momentum and “interact” with 1H

BoNH

CH

CC

HH H

Magnetization can betransferred between 1H, 13C and15N to establish connectivities

Chemical ShiftsJ-couplings (through bond)Dipolar couplings (through space)

NH

CH

CC

HH H Magnetization can be

transferred between 1H, 13C and15N to establish connectivities

HNCAHNCOCAHNCOCACB etcHSQC-TOCSY

They all use INEPT tranfersChemical ShiftsJ-couplings (through bond)Dipolar couplings (through space)

NH

CH

CC

HH H

NH

CH

CC

HH H

NH

CH

CC

HH H

3D HSQC - NOESY for Inter-residue contacts

e-

Concept 1: Some nuclei have non-zero spin quantum numbers.

Nuclei with odd mass numbers have half-integer spin quantum numbers.i.e. 13C, 1H, 31P are spin I = 1/2 17O is spin I = 5/2

Nuclei with an even mass number and an even charge number have spin quantumnumbers of zero.

ie. 12C

Nuclei with an even mass number and an odd charge number have integer spin quantum numbers.

i.e. 2H is spin I = 1

Electrons also have a spin quantum number of 1/2

e-

e-

Concept 2: Current passed through a coil induces a magnetic field.

e-e-

Concept 3: A changing magnetic field in a coilinduces a current.

QM picture

Mz

Classical picture

Concept 4: Placing nuclei with spin I = 1/2 into a magnetic field leads to a net magnetization aligned along the magnetic field axis.

Bo

Large external magnet

Net magnetizationaligned along Z-axisof the magnetic field

Bo

B1

Net magnetizationaligned along x-axisof the magnetic fieldafter application of B1field.

The B1 field is produced by a small coil in the NMRprobe which is placedin the bore of the largeexternal magnet.

Bo

B1

NMR probe

NMR magnet.

e-

e-

Concept 5: When the B1 field is turned on, the net magnetizationrotates down into the XY plane

Bo

z

xy

Concept 6: When the B1 field is turned off, the net magnetizationrelaxes back to the Z axis with the time constant T1

Bo

z

xy

T1

T1 is the “longitudinal” relaxation time constant which results from “spin-lattice” relaxation

Exponential Functions

y = e -x/t

y

x

y = 1- e -x/t

y

x

Mz = Mo (1- e -t/T1 )

Mz

t

z

xy

Bo

Concept 7: Individual spins precess about the magnetic field axis.

Precession frequency = Larmor frequency o = - Bo (MHz)

Concept 8: After magnetization is rotated into the xy plane by the B1 fieldproduced from a pulse through the coil, it will precess in the xy plane.

Bo

z

xy

x

y

x

Concept 9: The individual magnetization vectors whirling around in the xyplane represent a changing magnetic field and will induce a current in the sample coil which has its axis along the x-axis.

y

x

y

Concept 10: NMR signal is a Fourier transform of the oscillating current induced in the sample coil

x

y yx-y

-x

time

frequency

Chemical Shifts

Concept 12: Nuclear spins produce small magnetic fields

Concept 13: Electrons are spin I =1/2 particles. They produce small magnetic fieldswhich oppose the external magnetic field.

1H has a small chemical shift range (15 ppm). 113Cd has a large chemical shift range (300 ppm).

What is a ppm? Ppm = part per million

1H has a small chemical shift range (15 ppm).

1H 13C 15N400 MHz 100 MHz 30 MHz

1 ppm = 400 Hz15 ppm = 6000 Hz

15 ppm

a

b

a

b

CH3C-OH

Concept 14: The surrounding electrons shield the nuclear spins from the larger external Bo field. This results in a reduction in the energy spacingof the two energy levels and a lower Larmor frequency. This is thechemical shift.

CH3C-OH

frequency

x

y

e-e-

Concept 11: In a frame of reference that ROTATES at the Larmor (precession)frequency, magnetization that is placed along the x-axis does not move. (It simply relaxes back to the z-axis via T1 processes.)

a

b

a

b

CH3C-OH

100,010,000 Hz 100,000,000 Hz

Reference or carrier = 100,005,000 Hz

x

y

CH3

C-OH+5,000 Hz abovereference

-5,000 Hz belowreference

Concept 15: The nuclei with different chemical shifts and Larmor frequencieswill rotate around the z-axis at different speeds. T2 is the time constant forthe magnetization vectors to "dephase" in the xy plane.

CH3C-OH

frequency

reference frequency

NH

CH

CC

HH H

Chemical ShiftsJ-couplings (through bond)Dipolar couplings (through space)

T1 relaxationT2 relaxation

Structure

Dynamics

Acquire/2

General One Dimensional Experiment

Fourier Transform t1 -> f1

f1

t1

Acquire/2

General One Dimensional Experiment

Fourier Transform t1 -> f1

f1

t1

Acquire/2

General One Dimensional Experiment

Fourier Transform t1 -> f1

f1

t1

Fourier Transformationresolves multiple frequenciesthat overlap in the time domain

/2Acquire/2

General Two Dimensional Experiment

Fourier Transform t1 -> f1 and t2 -> f2

f2

t1 t2

f1

/2Acquire/2

General Two Dimensional Experiment

t1 t2/2

Acquire/2

t1 t2

/2Acquire/2

t1 t2

Vary t1Collect a series of 1D spectra

General Two Dimensional Experiment

t1

f2

Vary t1Collect a series of 1D spectra

Here, the intensities of and do notchange as a function of the t1 evolution time

General Two Dimensional Experiment

t1

f2

Vary t1Collect a series of 1D spectra

Whereas here, the intensity of is modulated as a function of the t1 evolution time

General Two Dimensional Experiment

t1

f2

Transpose and thenFourier transform in t1 dimension

General Two Dimensional Experiment

t1

f2

Transpose and thenFourier transform in t1 dimension

General Two Dimensional Experiment

f1

f2

Projection on f2 givesoriginal chemical shifts

General Two Dimensional Experiment

f1

f2

Projection on f1 yieldsnew information

General Two Dimensional Experiment

1H chemical shift

J coupling

1H chemical shift

Dipolarcoupling

1H chemical shift

13C chemicalshift

1H chemical shift

1H chemical shift