Nuclear Magnetic Resonance

Nuclear Magnetic Resonance A.) Introduction:

Nuclear Magnetic Resonance (NMR) measures the absorption of electromagnetic radiation in the radio-frequency region (~4-900 MHz)

- nuclei (instead of outer electrons) are involved in absorption process- sample needs to be placed in magnetic field to cause different

energy states

NMR was first experimentally observed by Bloch and Purcell in 1946 (received Nobel Prize in 1952) and quickly became commercially available and widely used.

Probe the Composition, Structure, Dynamics and Function of the Complete Range of Chemical Entities: from small organic molecules to large molecular weight polymers and proteins.

NMR is routinely and widely used as the preferred technique to rapidly elucidate the chemical structure of most organic compounds.

One of the One of the MOSTMOST Routinely used Analytical Techniques Routinely used Analytical Techniques

Typical Applications of NMR:1.) Structural (chemical) elucidation

‚ Natural product chemistry‚ Synthetic organic chemistry

- analytical tool of choice of synthetic chemists- used in conjunction with MS and IR

2.) Study of dynamic processes‚ reaction kinetics‚ study of equilibrium (chemical or structural)

3.) Structural (three-dimensional) studies‚ Proteins, Protein-ligand complexes‚ DNA, RNA, Protein/DNA complexes‚ Polysaccharides

4.) Drug Design ‚ Structure Activity Relationships by NMR

5) Medicine -MRI

MRI images of the Human Brain

NMR Structure of MMP-13 complexed to a ligand

O

O

O

O

OH

OO

O

HO

NH

OH

OO

O

O

Taxol (natural product)

2-phenyl-1,3-dioxep-5-ene2-phenyl-1,3-dioxep-5-ene

1313C NMR spectraC NMR spectra

11H NMR spectraH NMR spectra

NMRNMR: “fingerprint” of the compound’s chemical structure: “fingerprint” of the compound’s chemical structure

Protein Structures from NMRProtein Structures from NMR

2D NOESY Spectra at 900 MHz2D NOESY Spectra at 900 MHz Lysozyme Ribbon DiagramLysozyme Ribbon Diagram

1937 Rabi predicts and observes nuclear magnetic resonance1946 Bloch, Purcell first nuclear magnetic resonance of bulk sample1953 Overhauser NOE (nuclear Overhauser effect)1966 Ernst, Anderson Fourier transform NMR1975 Jeener, Ernst 2D NMR1985 Wüthrich first solution structure of a small protein (BPTI)

from NOE derived distance restraints1987 3D NMR + 13C, 15N isotope labeling of recombinant proteins

(resolution)1990 pulsed field gradients (artifact suppression)1996/7 new long range structural parameters:

- residual dipolar couplings from partial alignment in liquid crystalline media

- projection angle restraints from cross-correlated relaxation

TROSY (molecular weight > 100 kDa)Nobel prizes1944 Physics Rabi (Columbia)1952 Physics Bloch (Stanford), Purcell (Harvard)1991 Chemistry Ernst (ETH)2002 Chemistry Wüthrich (ETH)2003 Medicine Lauterbur (University of Illinois in Urbana ), Mansfield (University of Nottingham)

NMR HistoryNMR History

Some Suggested NMR ReferencesSome Suggested NMR References

“Spin Dynamics – Basics of Nuclear Magnetic Resonance” M. H. Levitt

“Basic One- and Two-Dimensional NMR Spectroscopy” Horst Friebolin

“Modern NMR Techniques for Chemistry Research” Andrew E. Derome

“NMR and Chemistry- an introduction to the fourier transform-multinuclear era” J. W. Akitt

“Nuclear Magnetic Resonance Spectroscopy” R. K Harris

“Protein NMR Spectroscopy: Principals and Practice” John Cavanagh, Arthur Palmer, Nicholas J. Skelton, Wayne Fairbrother

“Biomolecular NMR Spectroscopy” J. N. S. Evans

“NMR of Proteins and Nucleic Acids” Kurt Wuthrich

“Tables of Spectral Data for Structure Determination of Organic Compounds”Pretsch, Clerc, Seibl and Simon

“Spectrometric Identification of Organic Compounds” Silverstein, Bassler and Morrill

Integrated Spectral Data Base System for Organic Compoundshttp://www.aist.go.jp/RIODB/SDBS/menu-e.html The Basics of NMR Hypertext based NMR course http://www.cis.rit.edu/htbooks/nmr/nmr-main.htm

Educational NMR Software All kinds of NMR softwarehttp://www.york.ac.uk/depts/chem/services/nmr/edusoft.html

NMR Knowledge Base A lot of useful NMR linkshttp://www.spectroscopynow.com/

NMR Information Server News, Links, Conferences, Jobshttp://www.spincore.com/nmrinfo/

Technical Tidbits Useful source for the art of shimminghttp://www.acornnmr.com/nmr_topics.htm

BMRB (BioMagResBank) Database of NMR resonance assignmentshttp://www.bmrb.wisc.edu/

Some NMR Web SitesSome NMR Web Sites

http://www.aist.go.jp/RIODB/SDBS/menu-e.html

http://www.cis.rit.edu/htbooks/nmr/nmr-main.htm

http://www.york.ac.uk/depts/chem/services/nmr/edusoft.html

http://www.spectroscopynow.com/

http://www.spincore.com/nmrinfo/

http://www.acornnmr.com/nmr_topics.htm

http://www.bmrb.wisc.edu/



A Basic Concept in ElectroMagnetic TheoryA Basic Concept in ElectroMagnetic Theory

A Direct Application to NMR

A perpendicular external magnetic field will induce an electric current in a closed loop

An electric current in a closed loop will create a perpendicular magnetic field

Information in a NMR SpectraInformation in a NMR Spectra

1) Energy E = h

h is Planck constant is NMR resonance frequency 10-10 10-8 10-6 10-4 10-2 100 102

wavelength (cm)

-rays x-rays UV VIS IR -wave radio

ObservableObservable NameName QuantitativeQuantitative InformationInformation

Peak position Chemical shifts () (ppm) = obs –ref/ref (Hz) chemical (electronic)

environment of nucleus

Peak Splitting Coupling Constant (J) Hz peak separation neighboring nuclei (intensity ratios) (torsion angles)

Peak Intensity Integral unitless (ratio) nuclear count (ratio) relative height of integral curve T1 dependent

Peak Shape Line width = 1/T2 molecular motion peak half-height chemical exchange

uncertainty principaluncertainty in

energy

Basic NMR SpectrometerBasic NMR Spectrometer

sample lift

NMR Tube

RF coilscryoshims

shimcoils

Probe

Liquid He

Liquid N2

a) solenoid wound from superconducting niobium/tin or niobium/titanium wireb) kept at liquid helium temperature (4K), outer liquid N2 dewar

1) near zero resistance minimal current lose magnet stays at field for years without external power source

c) electric currents in the shim coils create small magnetic fields which compensate inhomogenieties

Cross-section of magnet

Superconducting solenoidUse up to 190 miles of wire!

spinner

magnet

Superconducting MagnetSuperconducting Magnet

1. Quantum Description

i. Nuclear Spin (think electron spin)a) Nucleus rotates about its axis (spin)b) Nuclei with spin have angular momentum (p)

1) quantized, spin quantum number I2) 2I + 1 states: I, I-1, I-2, …, -I3) identical energies in absence of

external magnetic fieldc) NMR “active” Nuclear Spin (I) = ½:

1H, 13C, 15N, 19F, 31P biological and chemical relevance Odd atomic mass

I = +½ & -½

NMR “inactive” Nuclear Spin (I) = 0:12C, 16O Even atomic mass &

number

Quadrupole Nuclei Nuclear Spin (I) > ½: 14N, 2H, 10B Even atomic mass & odd number

I = +1, 0 & -1

l

Theory of NMRTheory of NMR

ii. Magnetic Moment ()a) spinning charged nucleus creates a magnetic field

b) magnetic moment () is created along axis of the nuclear spin

= pwhere:

p – angular momentum – gyromagnetic ratio (different

value for each type of nucleus)

c) magnetic moment is quantized (m)m = I, I-1, I-2, …, -I

for common nuclei of interest: m = +½ & -½

Similar to magnetic field created by electric current flowing in a coil

Magnetic moment

Bo

= h / 4

Magnetic alignmentMagnetic alignment

In the absence of external field,each nuclei is energetically degenerate

Add a strong external field (Bo).and the nuclear magnetic moment: aligns with (low energy) against (high-energy)

iii. Energy Levels in a Magnetic Fielda) Zeeman Effect -Magnetic moments are oriented in one of two directions in

magnetic field

b) Difference in energy between the two states is given by:

E = h Bo / 2where:

Bo – external magnetic field units:Tesla (Kg

s-2 A-1) h – Planck’s constant 6.6260 x 10-34

Js

– gyromagnetic ratio unique value per nucleus

1H: 26.7519 x 107 rad T-1 s-

c) Frequency of absorption: = Bo / 2 (observed NMR frequency)

d) From Boltzmann equation: Nj/No = exp(-hBo/2kT)

2. Classical Description

i. Spinning particle precesses around an applied magnetic field

a) Angular velocity of this motion is given by:

o = Bo

where the frequency of precession of Larmor frequency is:

= Bo/2

Same as quantum mechanical description

Bo

= h / 4

Magnetic alignmentMagnetic alignment

In the absence of external field,each nuclei is energetically degenerate

Add a strong external field (Bo).and the nuclear magnetic moment: aligns with (low energy) against (high-energy)

Mo

y

x

z

x

y

z

Bo Bo

Bo > 0 E = h

Bo

Classic View:- Nuclei either align with or against external magnetic field along the z-axis.

- Since more nuclei align with field, net magnetization (Mo) exists parallel to external magnetic field

Quantum Description:- Nuclei either populate low energy (, aligned with field) or high energy (, aligned against field)

- Net population in energy level.

- Absorption of radio- frequency promotes nuclear spins from .

Net MagnetizationNet Magnetization

An NMR ExperimentAn NMR Experiment

Mo

y

x

z

x

y

z

Bo Bo

We have a net magnetization precessing about Bo at a frequency of o with a net population difference between aligned and unaligned spins.

Now What?

Perturbed the spin population or perform spin gymnasticsBasic principal of NMR experiments

B1 off…

(or off-resonance)

Mo

z

x

B1

z

x

Mxy

y y1

1

Right-hand rule

resonant condition: frequency (1) of B1 matches Larmor frequency (o)energy is absorbed and population of and states are perturbed.


And/Or:And/Or: Mo now precesses about B1

(similar to Bo) for as long as the B1 field is applied.

Again, keep in mind that individual spins flipped up or down(a single quanta), but Mo can have a continuous variation.

Classic View:- Apply a radio-frequency (RF) pulse a long the y-axis

- RF pulse viewed as a second field (B1), that the net magnetization (Mo) will precess about with an angular velocity of 1

-- precession stops when B1 turned off

Quantum Description:- enough RF energy has been absorbed, such that the population in / are now equal

- No net magnetization along the z-axis

B1 off…

(or off-resonance)

Mo

z

x

B1

z

x

Mxy

y y1

1

1 = B1

90o pulse

Bo > 0

E = h

Please Note: A whole variety of pulse widths are possible, not quantized dealing with bulk magnetization

Absorption of RF Energy or NMR RF Absorption of RF Energy or NMR RF PulsePulse


What Happens Next?

The B1 field is turned off and Mxy continues to precess about Bo at frequency o. z

x

Mxy

Receiver coil (x)

y

NMR signal

o

FID – Free Induction Decay

y y y

Mxy is precessing about z-axis in the x-y plane Time (s)

The oscillation of Mxy generates a fluctuating magnetic field which can be used to generate a current in a receiver coil to detect the NMR signal.


A magnetic field perpendicular to a circular loop will induce a current in the loop.

NMR Probe (antenna)

NMR Signal Detection - NMR Signal Detection - FIDFIDThe FID reflects the change in the magnitude of Mxy as

the signal is changing relative to the receiver along the y-axis

Again, the signal is precessing about Bo at its Larmor Frequency (o).

RF pulse along Y

Detect signal along X

NMR Signal Detection - Fourier NMR Signal Detection - Fourier TransformTransform

So, the NMR signal is collected in the Time - domain

But, we prefer the frequency domain.

Fourier Transform is a mathematical procedure that transforms time domain data into frequency domain

NMR Signal Detection - Fourier NMR Signal Detection - Fourier TransformTransformAfter the NMR Signal is Generated and the B1 Field is Removed, the

Net Magnetization Will Relax Back to Equilibrium Aligned Along the Z-axis

T2 relaxation

Two types of relaxation processes, one in the x,y plane and one along the z-axis

a) No spontaneous reemission of photons to relax down to ground state1) Probability too low cube of the frequency

b) Two types of NMR relaxation processes1) spin-lattice or longitudinal relaxation (T1)

i. transfer of energy to the lattice or solvent material

ii. coupling of nuclei magnetic field with magnetic fields created

by the ensemble of vibrational and rotational motion of the lattice or solvent.

iii. results in a minimal temperature increase in sample

iv. Relaxation time (T1) exponential decay

Mz = M0(1-exp(-t/T1))

Please Note: General practice is to wait 5xT1 for the system to have fully relaxed.

NMR RelaxationNMR Relaxation

2) spin-spin or transverse relaxation (T2)i. exchange of energy between excited

nucleus and low energy state nucleusii. randomization of spins or magnetic

moment in x,y-planeiii. related to NMR peak line-widthiv. relaxation time (T2)

Mx = My = M0 exp(-t/T2)

(derived from Heisenberg uncertainty principal)

Please Note: Line shape is also affected by the magnetic fields homogeneity

NMR SensitivityNMR Sensitivity

Bo = 0

Bo > 0 E = h

N / N = e E / kTBoltzmman distribution:

The applied magnetic field causes an energy difference between aligned() and unaligned() nuclei

The population (N) difference can be determined from

The E for 1H at 400 MHz (Bo = 9.5 T) is 3.8 x 10-5 Kcal / mol

Very Small !Very Small !~64 excess spins ~64 excess spins per million in lower per million in lower statestate

Low energy gap


EhBo /2

NMR signal depends on:1) Number of Nuclei (N) (limited to field homogeneity and

filling factor)2) Gyromagnetic ratio (in practice 3)3) Inversely to temperature (T)4) External magnetic field (Bo

2/3, in practice, homogeneity)5) B1

2 exciting field strengthN / N = e E / kT

Increase energy gap -> Increase population difference -> Increase NMR signal

E ≡ Bo≡

- Intrinsic property of nucleus can not be changed.

C)3 for 13C is 64xN)3

for 15N is 1000x

1H is ~ 64x as sensitive as 13C and 1000x as sensitive as 15N !

Consider that the natural abundance of 13C is 1.1% and 15N is 0.37%relative sensitivity increases to ~6,400x and ~2.7x105x !!

signal (s) 44BBoo22NBNB11g(g()/T)/T


Increase in Magnet Strength is a Major Means to Increase SensitivityBut at a significant cost!

~$800,000 ~$2,00,000 ~$4,500,000

Chemical Chemical ShiftShift

Up to this point, we have been treating nuclei in general terms.Simply comparing 1H, 13C, 15N etc.

If all 1H resonate at 500MHz at a field strength of 11.7T, NMR would not be very interesting

Beff = Bo - Bloc --- Beff = Bo( 1 - )

is the magnetic shielding of the nucleus

The chemical environment for each nuclei results in a unique local magnetic field (Bloc) for each nuclei:

a) Small local magnetic fields (Bloc) are generated by electrons as they circulate nuclei.1) Current in a circular coil generates a magnetic field

b) These local magnetic fields can either oppose or augment the external magnetic field1) Typically oppose external magnetic field2) Nuclei “see” an effective magnetic field (Beff) smaller then

the external field3) – magnetic shielding or screening constant

i. depends on electron density

ii. depends on the structure of the compoundBeff = Bo - Bloc --- Beff = Bo( 1 - )

HO-CH2-CH3

de-shielding high shieldingShielding – local field opposes Bo

= Bo/2

– reason why observe three distinct NMR peaks instead of one based on strength of B0

Chemical Chemical ShiftShift

c) Effect of Magnetic Anisotropy1) external field induces a flow (current) of electrons in system – ring current effect2) ring current induces a local magnetic field with shielding (decreased chemical shift) and deshielding (increased chemical shifts)

Decrease in chemical shifts

Increase in chemical shifts

The NMR scale (The NMR scale (, ppm), ppm)

- ref

= ppm (parts per million) ref

Instead use a relative scale, and refer all signals () in the spectrum to the signal of a particular compound (ref).

Bo >> Bloc -- MHz compared to Hz

Comparing small changes in the context of a large number is cumbersome

Tetramethyl silane (TMS) is a common reference chemicalH3C Si CH3

CH3

CH3

IMPORTANT: absolute frequency is field dependent ( = Bo / 2)

The NMR scale (The NMR scale (, ppm), ppm)

Chemical shift) is a relative scale so it is independent of Bo. Same chemical shift at 100 MHz vs. 900 MHz magnet

IMPORTANT: absolute frequency is field dependent ( = Bo / 2)

At higher magnetic fields an NMR spectra will exhibit the same chemical shifts but with higher resolution because of the higher frequency range.

NMR Spectra TerminologyNMR Spectra Terminology

Increasing field (Bo)Increasing frequency ()Increasing Increasing energy (E, consistent with UV/IR)

1H 13C 2H600 MHz 150 MHz 92 MHz

TMS

CHCl3

7.27 0 ppmincreasing decreasing low field high field down field up fieldhigh frequency () low frequencyde-shielding high shielding Paramagnetic diamagnetic

Chemical Shift TrendsChemical Shift Trends

Carbon chemical shifts have similar trends, but over a larger sweep-width range (0-200 ppm)

For protons, ~ 15 ppm:For carbon, ~ 220 ppm:

Chemical Shift TrendsChemical Shift Trends

0TMS

ppm

210 7 515

Aliphatic

Alcohols, protons to ketones

Olefins

AromaticsAmidesAcids

Aldehydes

ppm

50150 100 80210

Aliphatic CH3,CH2, CH

Carbons adjacent toalcohols, ketones

Olefins

Aromatics,conjugated alkenes

C=O of Acids,aldehydes, esters

0TMS

C=O inketones

CHARACTERISTIC PROTON CHEMICAL SHIFTS

Type of Proton Structure Chemical Shift, ppm

Cyclopropane C3H6 0.2

Primary R-CH3 0.9

Secondary R2-CH2 1.3

Tertiary R3-C-H 1.5

Vinylic C=C-H 4.6-5.9

Acetylenic triple bond,CC-H 2-3

Aromatic Ar-H 6-8.5

Benzylic Ar-C-H 2.2-3

Allylic C=C-CH3 1.7

Fluorides H-C-F 4-4.5

Chlorides H-C-Cl 3-4

Bromides H-C-Br 2.5-4

Iodides H-C-I 2-4

Alcohols H-C-OH 3.4-4

Ethers H-C-OR 3.3-4

Esters RCOO-C-H 3.7-4.1

Esters H-C-COOR 2-2.2

Acids H-C-COOH 2-2.6

Carbonyl Compounds H-C-C=O 2-2.7

Aldehydic R-(H-)C=O 9-10

Hydroxylic R-C-OH 1-5.5

Phenolic Ar-OH 4-12

Enolic C=C-OH 15-17

Carboxylic RCOOH 10.5-12

Amino RNH2 1-5

Common Chemical Shift Ranges

Carbon chemical shifts have similar trends, but over a larger sweep-width range (0-200 ppm)

Predicting Chemical Shift AssignmentsPredicting Chemical Shift Assignments

Numerous Experimental NMR Data has been compiled and general trends identified

• See: “Tables of Spectral Data for Structure Determination of Organic Compounds” Pretsch, Clerc, Seibl and Simon

“Spectrometric Identification of Organic Compounds” Silverstein, Bassler and Morrill

• Spectral Databases: Aldrich/ACD Library of FT NMR Spectra Sadtler/Spectroscopy (UV/Vis, IR, MS, GC and NMR)

Ongoing effort to predict chemical shifts from first principals (quantum mechanical description of factors contributing to chemical shifts)


Empirical Chemical Shift Trends (Databases) Have Been Incorporated Into A Variety of Software Applications

Example: ChemDraw• Program that allows you to generate a 2D sketch of any compound• can also predict 1H and 13C chemical shifts

matches sub-fragments of structure to structures in database

H

H

H

H

H

H6.44

6.44

6.44

6.44

5.22

5.22

Estimation Quality: blue = good, magenta = medium, red = rough 0123456PPM

FulveneProtocol of the H-1 NMR Prediction:

Node Shift Base + Inc. Comment (ppm rel. to TMS)

H 6.44 5.25 1-ethylene 1.24 1 -C=C gem -0.05 1 -C=C trans H 6.44 5.25 1-ethylene -0.05 1 -C=C trans 1.24 1 -C=C gem H 6.44 5.25 1-ethylene 1.24 1 -C=C gem -0.05 1 -C=C trans H 6.44 5.25 1-ethylene -0.05 1 -C=C trans 1.24 1 -C=C gem H 5.22 5.25 1-ethylene -0.03 2 -C=C c + t H 5.22 5.25 1-ethylene -0.03 2 -C=C c + t


How Does the Predicted Results Compare to Experimental Data?

Parameter Experimental ( ppm) Predicted (ppm) D(A) 6.22 6.44D(B) 6.53 6.44 D(C) 5.85 5.22

Typical accuracy

A number of factors can affect prediction: Similarity of structures in reference database Solvent Temperature structure/conformation additive nature of parts towards the whole

Coupling ConstantsCoupling Constants

Energy level of a nuclei are affected by covalently-bonded neighbors spin-states

13C

1H 1H 1H

one-bond

three-bond

I SS

S

I

I

J (Hz)

Spin-States of covalently-bonded nuclei want to be aligned.

The magnitude of the separation is called coupling constant (J) and has units of Hz.

+J/4

-J/4

+J/4

a) through-bond interaction that results in the splitting of a single peak into multiple peaks of various intensities 1) The spacing in hertz (hz) between the peaks is a constant

i. coupling constant (J)b) bonding electrons convey spin states of bonded nuclei

1) spin states of nuclei are “coupled”2) alignment of spin states of bonded nuclei affects energy of

the ground () and excited states () of observed nuclei 3) Coupling pattern and intensity follows Pascal’s triangle

11 1

1 2 11 3 3 1

1 4 6 4 11 5 10 10 5 1

1 6 15 20 15 6 11 7 21 35 35 21 7 1

Coupling ConstantsCoupling Constants

Pascal's triangle

ab

singlet doublet triplet quartet pentet 1:1 1:2:1 1:3:3:1 1:4:6:4:1

Common NMR Splitting Patterns

Coupling Rules:1. equivalent nuclei do not interact2. coupling constants decreases with separation ( typically 3 bonds)3. multiplicity given by number of attached equivalent protons (n+1)4. multiple spin systems multiplicity (na+1)(nb+1) 5. Relative peak heights/area follows Pascal’s triangle6. Coupling constant are independent of applied field strength

IMPORTANT: Coupling constant pattern allow for the identification of bonded nuclei.

Multiplets consist of 2nI + 1 lines I is the nuclear spin quantum number (usually 1/2) andn is the number of neighboring spins.

Karplus Equation – Coupling Constants Karplus Equation – Coupling Constants

Relates coupling constant toTorsional angle.

Used to solve Structures!

J = const. + 10Cos

a) Interaction between nuclear spins mediated through empty space (5Å) like ordinary bar magnets

b) Important: effect is time-averagedc) Gives rise to dipolar relaxation (T1 and T2) and specially to

cross-relaxation

Perturb 1H spin populationaffects 13C spin population NOE effect

Nuclear Overhauser Effect (NOE)Nuclear Overhauser Effect (NOE)


Nuclear Overhauser Effect (NOE, ) – the change in intensity of an NMR resonance when the transition of another are perturbed, usually by saturation.

Saturation – elimination of a population difference between transitions (irradiating one transition with a weak RF field)

i = (I-Io)/Io

where Io is thermal equilibrium intensity

N N

N+

N-X

X A

A

irradiate

Populations and energy levels of a homonuclear AX system (large chemical shift difference)

Observed signals only occur from single-quantum transitions


N+½

I

I S

S

Populations and energy levels immediately following saturation of the S transitions

N+½N-½

N-½

Saturated(equal population)

Saturated(equal population)

saturate

W1

A

W1A

W1X

W1X

W2

W0

Observed signals only occur from single-quantum transitions

Relaxation back to equilibrium can occur through:Zero-quantum transitions (W0)Single quantum transitions (W1)Double quantum transitions (W2)

N-½

N+½

N+½

N-½

The observed NOE will depend on the “rate” of these relaxation pathwaysThe observed NOE will depend on the “rate” of these relaxation pathways

Nuclear Overhauser Effect (NOE)Nuclear Overhauser Effect (NOE)Mechanism for Relaxation

• Dipolar coupling between nuclei– local field at one nucleus is due to the presence of the other– depends on orientation of the whole molecule

• Dipolar coupling, T1 and NOE are related through rotational correlation time (c)

– rotational correlation is the time it takes a molecule to rotate one radian (360o/2).

• Relaxation or energy transfers only occurs if some frequencies of motion match the frequency of the energy of transition

– the available frequencies for a molecule undergoing Brownian tumbling depends on tc

62262

62260

62261

12

))(1(

12

2

))(

3

3

)1(

3

rrW

rrW

rrW

c

cXA

c

c

cXA

c

c

cA

cA

NOE is dependent on the distance (1/r6) separating the two dipole coupled nuclei

Important: the effect is time-averaged!

2D NOESY (Nuclear Overhauser Effect)2D NOESY (Nuclear Overhauser Effect)

Relative magnitude of the cross-peak is related to the distance (1/r6) between the protons (≥ 5Ǻ).

NOE is a relaxation factor that builds-up duringThe “mixing-time (tm)

2D NOESY Spectra at 900 MHz2D NOESY Spectra at 900 MHz Lysozyme Ribbon DiagramLysozyme Ribbon Diagram

NMR Structure Determination

NOE Data Is the Fundamental Piece of Information to Determine Any Structure (DNA, RNA, Protein, small molecule)

Continuous Wave (CW) vs. Pulse/Fourier TransformContinuous Wave (CW) vs. Pulse/Fourier Transform

NMR Sensitivity Issue

A frequency sweep (CW) to identify resonance is very slow (1-10 min.)Step through each individual frequency.

Pulsed/FT collect all frequencies at once in time domain, fast (N x 1-10 sec)

Increase signal-to-noise (S/N) by collecting multiple copies of FID and averaging signal.

S/N number of scans

NMR Data Detection and ProcessingNMR Data Detection and Processing

A radiofrequency pulse is a combination of a wave (cosine) of frequency wo and a step function

i. NMR Pulsea) In FT-NMR, how are all the individual nuclei excited simultaneously?b) RF pulses are typically short-duration (secs)

1) produces bandwidth (1/4) centered around single frequency2) shorter pulse width broader frequency bandwidth

i. Heisenberg Uncertainty Principal: t

FT

* =tp

Pulse length (time, tp)

The Fourier transform indicates the pulse covers a range of frequencies

NMR PulseNMR Pulse

z

x

Mxy

y

z

x

y

Mo

B1

ttp

t = * tp * B1

NMR pulse length or Tip angle (tp)

The length of time the B1 field is on => torque on bulk magnetization (B1)

A measured quantity – instrument and sample dependent.

NMR PulseNMR Pulse

z

x

Mxy

y

z

x

y

Mo / 2

Some useful common pulses

90o

Maximizes signal in x,y-planewhere NMR signal detected

z

x

-Moy

z

x

y

Mo

180o

90o pulse

180o pulse

Inverts the spin-population.No NMR signal detected

Can generate just about any pulse width desired.

0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00t1 sec

SR = 1 / (2 * SW)

The Nyquist Theorem says that we have to sample at least twice as fast as the fastest (higher frequency) signal.

Sample Rate

- Correct rate, correct frequency-½ correct rate, ½ correct frequency Folded peaks!Wrong phase!

SR – sampling rate

ii. Sampling the Audio Signala) Collect Digital data by periodically sampling signal voltage

1) ADC – analog to digital converterb) To correctly represent Cos/Sin wave, need to collect data at least twice as fast as the signal frequencyc) If sampling is too slow, get folded or aliased peaks

Correct Spectra

Spectra with carrier offset resulting in peak folding or aliasing

Sweep Width (range of radio-frequencies monitored for nuclei absorptions)

234 233 232 231 230 229 228 227 226 225 224 223f1 ppm

carrier

carrier

iii. Quadrature detectiona) Frequency of B1 (carrier) is set to the center of the spectra.

1) Small pulse length to excite the entire spectrum2) Minimizes folded noise

b) How to differentiate between peaks upfield and downfield from carrier?1) observed peak frequencies are all relative to the carrier

frequencyc) If carrier is at edge of spectra, then peaks are all positive or negative relative to carrier

1) Excite twice as much noise, decrease S/N

How to differentiate between magnetization that precesses clockwise and counter clockwise?

same frequency relative to the carrier, but opposite sign.

(B1)

B

F

B

F

PH = 0

PH

= 9

0PH = 0

PH = 90

F

F

S

S

Use two detectors 90o out of phase.

Phase of Peaksare different.

iv. Window Functionsa) Emphasize the signal and decrease the noise by applying a mathematical function to the FID.b) NMR signal is decaying by T2 as the FID is collected.

0 0.10 0.20 0.30 0.40 0.50t1 sec

Good stuff Mostly noise

F(t) = 1 * e - ( LB * t ) – line broadening Effectively adds LB in Hz to peak

Line-widths

Sensitivity Resolution

0 0.10 0.20 0.30 0.40 0.50t1 sec

1080 1060 1040 1020 1000 980 960 940 920 900f1 ppm

0 0.10 0.20 0.30 0.40 0.50t1 sec0 0.10 0.20 0.30 0.40 0.50

t1 sec

1080 1060 1040 1020 1000 980 960 940 920 900f1 ppm

FT FT

LB = -1.0 HzLB = 5.0 Hz

Can either increase S/N or Resolution Not Both!

Increase Sensitivity Increase Resolution

Dwell time DW

TD

AQ = TD * DW= TD/2SWH

Total Data Acquisition Time (AQ):

Should be long enough to allow complete delay of FID

Higher Digital Resolution requires longer acquisition times

v. NMR data sizea) Analog signal is digitized by periodically monitoring the induced current in the

receiver coilb) How many data points are collected? What is the time delay between data points c) Digital Resolution (DR) – number of Hz per point in the FID for a given spectral

width. DR = SW / TD

where:SW – spectral width (Hz)TD – data size (points)

d) Dwell Time (DW) – constant time interval between data points.SW = 1 / (2 * DW)

e) From Nyquist Theorem, Sampling Rate (SR) SR = 1 / (2 * SW)

f) Dependent Valuables

231.40 231.39 231.38 231.37 231.36 231.35 231.34 231.33 231.32 231.31 231.30 231.29 231.28 231.27 231.26 231.25 231.24f1 ppm

231.42 231.40 231.38 231.36 231.34 231.32 231.30 231.28 231.26 231.24 231.22 231.20f1 ppm

0 0.20 0.40 0.60 0.80 1.00 1.2 1.4 1.6 1.8 2.0 2.2t1 sec

8K data 8K zero-fill

8K FID 16K FID

No zero-filling 8K zero-filling

vi. Zero Fillinga) Improve digital resolution by adding zero data points at end of FID

vii. NMR Peak Integration or Peak Areaa) The relative peak intensity or peak area is proportional to the number of protons

associated with the observed peak.b) Means to determine relative concentrations of multiple species present in an NMR

sample.

HO-CH2-CH3 12

3

Relative peak areas = Number of protons

Integral trace

i. NMR time scale refers to the chemical shift time scalea) remember – frequency units are in Hz (sec-1) time scaleb) exchange rate (k)c) differences in chemical shifts between species in exchange indicate the exchange rate.

d) For systems in fast exchange, the observed chemical shift is the average of the individual species chemical shifts.

Time Scale Chem. Shift () Coupling Const. (J) T2 relaxationSlow k << A- B k << JA- JB k << 1/ T2,A- 1/ T2,B

Intermediate k = A - B k = JA- JB k = 1/ T2,A- 1/ T2,B

Fast k >> A - B k >> JA- JB k >> 1/ T2,A- 1/ T2,B

Range (Sec-1) 0 – 1000 0 –12 1 - 20

obs = f11 + f22

f1 +f2 =1where:

f1, f2 – mole fraction of each species1,2 – chemical shift of each species

Exchange Rates and NMR Time ScaleExchange Rates and NMR Time Scale

ii. Effects of Exchange Rates on NMR data

k = (he-ho)

k = (o2 - e

2)1/2/21/2

k = o / 21/2

k = o2 /2(he - ho)

k – exchange rateh – peak-width at half-height – peak frequencye – with exchangeo – no exchange

i. NMR pulse sequencesa) composed of a series of RF pulses, delays, gradient pulses and phasesb) in a 1D NMR experiment, the FID acquisition time is the time domain (t1)c) more complex NMR experiments will use multiple “time-dimensiona” to obtain data and simplify the analysis.d) Multidimensional NMR experiments may also use multiple nuclei (2D, 13C,15N) in addition to 1H, but usually detect 1H)

1D NMR Pulse Sequence

MultiDimensional NMRMultiDimensional NMR

ii. Creating Multiple Dimensions in NMRa) collect a series of FIDS incremented by a second time domain (t1)

1) evolution of a second chemical shift or coupling constant occurs

during this time periodb) the normal acquisition time is t2.c) Fourier transformation occurs for both t1 and t2, creating a two- dimensional (2D) NMR spectra

Relative appearance of each NMR spectra will be modulated by the t1 delay

Collections of FIDs with t1 modulations

Fourier Transform t2 obtain series of NMR spectra modulated by t1

Looking down t1 axis, each point has characteristics of time domain FID

Fourier Transform t1 obtain 2D NMR spectra

Peaks along diagonal are normal 1D NMR spectra

Cross-peaks correlate two diagonal peaks by J-coupling or NOE interactions

Contour map (slice at certain threshold) of 3D representation of 2D NMR spectra. (peak intensity is third dimension

ii. Creating Multiple Dimensions in NMRd) During t1 time period, peak intensities are modulated at a frequency corresponding to the chemical shift of its coupled partner.e) In 2D NMR spectra, diagonal peaks are normal 1D peaks, off-diagonal or

cross-peaks indicate a correlation between the two diagonal peaks

iii. Example: 2D NOESY NMR Spectraa) diagonal peaks are correlated by through-space dipole-dipole interaction (NOE)b) NOE is a relaxation factor that builds-up during the “mixing-time” (m)c) relative magnitude of the cross-peak is related to the distance (1/r6) between the protons (≥ 5Å).

2D NOESY NMR Pulse Sequence Diagonal peaks corresponds to 1D NMR spectra

Cross peaks correlate diagonal peaks by J-coupling or NOEs

Indirect (second) 1H chemical evolves during t1

NOE intensity evolves during m

Direct (observed) 1H chemical evolves during t2

iv. 3D & 4D NMR Spectraa) similar to 2D NMR with either three or four time domains.b) additional dimensions usually correspond to 13C & 15N chemical shifts.c) primarily used for analysis of biomolecular structures

1) disperses highly overlapped NMR spectra into 3 & 4 dimensions, simplifies analysis.

d) view 3D, 4D experiments as collection of 2D spectra.e) one experiment may take 2.5 to 4 days to collect.

1) diminished resolution and sensitivity

Spread peaks out by 15N chemical shift of amide N attached to NH

Further spread peaks out by 13C chemical shift of C attached to CH

Protein NMRProtein NMR

How do you assign aprotein NMR spectra?

A collection of “COSY”-likeexperiments that sequentiallywalk down the proteins’ backbone

3D-NMR experiments thatRequire 13C and 15N labeledProtein sample

Detect couplings to NHDetect couplings to NH


Assignment strategyWe know the primary sequence of the protein.

Connect the overlapping correlation between NMR experiments

Correlation of the Ci & Ci-1

and Ci & Ci-1 sequentially aligns each pair of NHs in the protein’s sequence.

Amide “Strips” from the 3D CBCANH (right) and CBCA(CO)NH (left) experiment arranged in sequential order


Molecular-weight Problem

Higher molecular-weight –> more atoms –> more NMR resonance overlap

More dramatic:NMR spectra deteriorate with increasingmolecular-weight.

MW increases -> correlation time increases-> T2 decreases -> line-width increases

NMR lines broaden to the point of not being detected!

With broad lines, correlations (J, NOE) become less-efficient


How to Solve the Molecular-weight Problem?

1) Deuterium label the protein.• replace 1H with 2H and remove efficient relaxation paths• NMR resonances sharpen• problem: no hydrogens -> no NOEs -> no structure• actually get exchangeable (NH –NH) noes can augment with specific 1H labeling

2) TROSY• line-width is field dependent

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Nuclear Magnetic Resonance