Slide 1

Transcript Slide 1

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 MOST 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  S tructure A ctivity R elationships by NMR 5) Medicine -MRI O NH O OH O O O OH O HO O O O O

Taxol (natural product) NMR Structure of MMP-13 complexed to a ligand MRI images of the Human Brain

NMR

: “fingerprint” of the compound’s chemical structure

2-phenyl-1,3-dioxep-5-ene 1 H NMR spectra 13 C NMR spectra

Protein Structures from NMR

2D NOESY Spectra at 900 MHz Lysozyme Ribbon Diagram

NMR History

1937 1946 1953 1966 1975 1985 Rabi predicts and observes nuclear magnetic resonance Bloch, Purcell first nuclear magnetic resonance of bulk sample Overhauser NOE (nuclear Overhauser effect) Ernst, Anderson Fourier transform NMR Jeener, Ernst 2D NMR Wüthrich first solution structure of a small protein (BPTI) from NOE derived distance restraints 1987 1990 3D NMR + 13C, 15N isotope labeling of recombinant proteins (resolution) pulsed field gradients (artifact suppression) 1996/7 new

Nobel prizes

long range

crystalline media structural parameters: - residual dipolar couplings from partial alignment in liquid - projection angle restraints from cross-correlated relaxation TROSY (molecular weight > 100 kDa) 1944 1952 1991 2002 2003

Physics

Rabi (Columbia)

Physics Chemistry Chemistry Medicine

Bloch (Stanford), Purcell (Harvard) Ernst (ETH) Wüthrich (ETH) Lauterbur (University of Illinois in Urbana ), Mansfield (University of Nottingham)

Some 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

Some NMR Web Sites

Integrated Spectral Data Base System for Organic Compounds http://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 software http://www.york.ac.uk/depts/chem/services/nmr/edusoft.html

NMR Knowledge Base http://www.spectroscopynow.com/ A lot of useful NMR links NMR Information Server http://www.spincore.com/nmrinfo/ News, Links, Conferences, Jobs Technical Tidbits Useful source for the art of shimming http://www.acornnmr.com/nmr_topics.htm

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

A 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 Spectra

1) Energy E = h u g -rays x-rays UV VIS IR m -wave radio h u is Planck constant is NMR resonance frequency 10 -10 10 -8 10 -6 10 -4 10 -2 wavelength (cm) 10 0 10 2

Observable

Peak position

Name

Chemical shifts ( d )

Quantitative

d (ppm) = u obs – u ref / u ref (Hz)

Information

chemical (electronic) environment of nucleus Peak Splitting Coupling Constant (J) Hz peak separation neighboring nuclei (intensity ratios) (torsion angles) Peak Intensity Integral unitless (ratio) relative height of integral curve Peak Shape Line width Du = 1/ p T 2 peak half-height nuclear count (ratio) T 1 dependent molecular motion chemical exchange uncertainty principal uncertainty in energy

Basic NMR Spectrometer

Superconducting Magnet

a) b) c) solenoid wound from superconducting niobium/tin or niobium/titanium wire kept at liquid helium temperature (4K), outer liquid N 2 1) near zero resistance  minimal current lose dewar  magnet stays at field for years without external power source electric currents in the shim coils create small magnetic fields which compensate inhomogenieties Cross-section of magnet magnet spinner sample lift NMR Tube RF coils cryoshims shimcoils Probe

Superconducting solenoid

Use up to 190 miles of wire!

Liquid N 2 Liquid He

Theory of NMR

Quantum Description

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

2) 2 I + 1 states: I, I-1, I-2, …, -I 3) identical energies in absence of external magnetic field

NMR “active” Nuclear Spin (I) = ½: 1 H, 13 C, 15 N, 19 F, 31 P   biological and chemical relevance Odd atomic mass I = +½ & -½ NMR “inactive” Nuclear Spin (I) = 0: 12 C, 16 O  Even atomic mass & number Quadrupole Nuclei Nuclear Spin (I) > ½: 14 N, 2 H, 10 B  Even atomic mass & odd number I = +1, 0 & -1

ii. Magnetic Moment (

)

a) spinning charged nucleus creates a magnetic field Magnetic moment

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

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

where: p g – 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

Magnetic alignment

h / 4

p In the absence of external field, each nuclei is energetically degenerate Add a strong external field (B o ).

and the nuclear magnetic moment: aligns with (low energy) against (high-energy)

B o

iii. Energy Levels in a Magnetic Field

a) Zeeman Effect -Magnetic moments are oriented in one of two directions in magnetic field b) c) d) Difference in energy between the two states is given by: D

E =

h B o / 2

p where: B o h – external magnetic field – Planck’s constant  g –  units:Tesla (Kg s -2 6.6260 x 10 -34 gyromagnetic ratio  Js A -1 ) unique value per nucleus Frequency of absorption: n

B o

1 H: 26.7519 x 10 7

/ 2

p rad T -1 s -

(observed NMR frequency)

From Boltzmann equation: N j /N o = exp( g hB o /2 p kT)

Classical Description

Spinning particle precesses around an applied magnetic field a) Angular velocity of this motion is given by:

o =

B o

where the frequency of precession of Larmor frequency is: n

B o /2

Same as quantum mechanical description

Magnetic alignment

h / 4

p In the absence of external field, each nuclei is energetically degenerate Add a strong external field (B o ).

and the nuclear magnetic moment: aligns with (low energy) against (high-energy)

B o

Net Magnetization

Classic View:

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

- Since more nuclei align with field, net magnetization (M o ) 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

level.

energy - Absorption of radio frequency promotes nuclear spins from

a  b

z x

B o

M o

z x

B o B o > 0

b a

B o

E = h

An NMR Experiment

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

z z

M o

x x y y

B o B o Now What?

Perturbed the spin population or perform spin gymnastics Basic principal of NMR experiments

An NMR Experiment

resonant condition:

frequency ( w 1 ) of B 1 matches energy is absorbed and population of a and b

Larmor

frequency ( w o ) states are perturbed.

z z

B 1

M o B 1 off…

(or off-resonance)

y x

M xy

And/Or: M

now precesses about B

(similar to B

) for as long as the B

field is applied.

Again, keep in mind that individual spins flipped up or down (a single

quanta

), but

M o

can have a continuous variation.

Right-hand rule

Absorption of RF Energy or NMR RF Pulse

Classic View:

- Apply a radio-frequency (RF) pulse a long the y-axis - RF pulse viewed as a second field (B 1 ), that the net magnetization (M o ) will precess about with an angular velocity of

1 - precession stops when B 1 turned off

1 B 1

M o

Quantum Description:

- enough RF energy has been absorbed, such that the population in

are now equal - No net magnetization along the z-axis

z x 90 o pulse

B 1 off… (or off-resonance)

1 =

B 1

B o > 0

b a

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

M xy

E = h

An NMR Experiment

What Happens Next?

The B 1 field is turned off and M xy

continues to precess about B o at frequency w o.

o M xy

Receiver coil (x) 

NMR signal

Mxy is precessing about z-axis in the x-y plane FID – Free Induction Decay Time (s) y y y

An NMR Experiment

The oscillation of

M xy

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

NMR Probe (antenna)

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

NMR Signal Detection - FID

The FID reflects the change in the magnitude of Mxy as the signal is changing relative to the receiver along the y-axis

RF pulse along Y Detect signal along X

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

NMR Signal Detection - Fourier Transform

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 Transform

After the NMR Signal is Generated and the B1 Field is Removed, the Net Magnetization Will Relax Back to Equilibrium Aligned Along the Z-axis

T 2 relaxation

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

NMR Relaxation

a) b) No spontaneous reemission of photons to relax down to ground state

1) Probability too low  cube of the frequency

Two types of NMR relaxation processes

1) spin-lattice or longitudinal relaxation (T 1 ) 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 (T 1 )  exponential decay

M z = M 0 (1-exp(-t/T 1 ))

Please Note: General practice is to wait 5xT 1 for the system to have fully relaxed.

2) spin-spin or transverse relaxation (T 2 ) i. exchange of energy between excited nucleus and low energy state nucleus ii. randomization of spins or magnetic moment in x,y-plane iii. related to NMR peak line-width iv. relaxation time (T 2 )

M x = M y = M 0 exp(-t/T 2 )

( derived from Heisenberg uncertainty principal) Please Note: Line shape is also affected by the magnetic fields homogeneity

NMR Sensitivity

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

B o > 0

b Low energy gap D

E = h

n a

B o = 0

The population (

difference can be determined from Boltzmman distribution:

/ N

= e

E / kT

The D E for 1 H at 400 MHz (

B o

= 9.5 T) is 3.8 x 10 -5 Kcal / mol N a / N b = 1.000064

Very Small !

~64 excess spins per million in lower state

NMR Sensitivity

NMR signal depends on: signal (s) % 2) Gyromagnetic ratio (in practice g 3 ) g 4 B o 2 NB 1 g( u )/T 1) Number of Nuclei (N) (limited to field homogeneity and filling factor) 3) Inversely to temperature (T) 4) External magnetic field (B o 2/3 , in practice, homogeneity) 5) B 1 2 exciting field strength

/ N

= e

E / kT

= g

h B o / 2

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

≡

B o

≡ g g Intrinsic property of nucleus can not be changed.

(g H /g C ) 3 for 13 C is 64x (g H /g N ) 3 for 15 N is 1000x 1 H is ~ 64x as sensitive as 13 C and 1000x as sensitive as 15 N !

Consider that the natural abundance of 13 C is 1.1% and 15 N is 0.37% relative sensitivity increases to ~6,400x and ~2.7x10

5 x !!

NMR Sensitivity

Increase in Magnet Strength is a Major Means to Increase Sensitivity

But at a significant cost!

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

Chemical Shift

Up to this point, we have been treating nuclei in general terms.

Simply comparing 1 H, 13 C, 15 N etc.

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

chemical environment

for each nuclei results in a unique magnetic field (B loc ) for each nuclei: local

B eff = B o - B loc --- B eff = B o ( 1 -

)

s is the

magnetic shielding

of the nucleus

Chemical Shift

a) b) Small local magnetic fields (B loc ) are generated by electrons as they circulate nuclei.

1) Current in a circular coil generates a magnetic field

These local magnetic fields can either oppose or augment the external magnetic field

1) 2) 3) Typically oppose external magnetic field Nuclei “see” an effective magnetic field (B eff ) smaller then the external field s – magnetic shielding or screening constant i. depends on electron density ii. depends on the structure of the compound

B eff = B o - B loc --- B eff = B o ( 1 -

) HO-CH 2 -CH 3

– reason why observe three distinct NMR peaks instead of one based on strength of B 0

B o /2

p de-shielding high shielding

Shielding – local field opposes B

c) Effect of Magnetic Anisotropy 1) external field induces a flow (current) of electrons in current effect

system – ring 2) 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 (

, ppm)

B o >> B loc -- MHz compared to Hz Comparing small changes in the context of a large number is cumbersome d

ref

ref ppm (parts per million)

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

IMPORTANT: absolute frequency is field dependent (

B o / 2

) CH 3

Tetramethyl silane

(

TMS

) is a common reference chemical

H 3 C Si CH 3 CH 3

The NMR scale (

, ppm)

Chemical shift

(d)

is a relative scale so it is independent of B

. Same chemical shift at 100 MHz vs. 900 MHz magnet

IMPORTANT: absolute frequency is field dependent (

B o / 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 Terminology

TMS CHCl 3 7.27 0 ppm increasing d decreasing d low field high field down field up field high frequency ( u ) low frequency de-shielding high shielding Paramagnetic diamagnetic 600 MHz 1 H 150 MHz 13 C 92 MHz 2 H Increasing field (B o ) Increasing frequency ( u ) Increasing g Increasing energy (E, consistent with UV/IR)

Chemical Shift Trends

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

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

Chemical Shift Trends

Acids Aldehydes Alcohols, protons a Aromatics Amides Olefins to ketones Aliphatic

15 10 7

C=O in ketones Aromatics, conjugated alkenes Olefins

5 2 0 TMS ppm

Aliphatic CH 3 , CH 2 , CH

210 150

C=O of Acids, aldehydes, esters

100 80 50

Carbons adjacent to alcohols, ketones

0 TMS ppm

Common Chemical Shift Ranges

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

CHARACTERISTIC PROTON CHEMICAL SHIFTS Type of Proton

Cyclopropane Primary Secondary Tertiary Vinylic Acetylenic Aromatic Benzylic Allylic Fluorides Chlorides Bromides Iodides Alcohols Ethers Esters Esters Acids Carbonyl Compounds Aldehydic Hydroxylic Phenolic Enolic Carboxylic Amino

Structure

C 3 H 6 R-C

3 R 2 -C

2 R 3 -C-

C=C-

triple bond,CC-

Ar-

Ar-C-

C=C-C

-C-F

-C-Cl

-C-Br

-C-I

-C-OH

-C-OR RCOO-C-

H H

-C-COOR

-C-COOH

-C-C=O R-(

-)C=O R-C-O

Ar-O RN

H H

C=C-O

RCOO

Chemical Shift, ppm

0.2

0.9

1.3

1.5

4.6-5.9

2-3 6-8.5

2.2-3 1.7

4-4.5

3-4 2.5-4 2-4 3.4-4 3.3-4 3.7-4.1

2-2.2

2-2.6

2-2.7

9-10 1-5.5

4-12 15-17 10.5-12 1-5

Predicting 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)

Predicting Chemical Shift Assignments

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 1 H and 13 C chemical shifts  matches sub-fragments of structure to structures in database

Fulvene

5.22

H H 5.22

6.44

H H 6.44

6.44

H H 6.44

Estimation Quality: blue = good, magenta = medium, red = rough 6 5 Protocol 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 4 PPM 3 2 1 0

Predicting Chemical Shift Assignments

How Does the Predicted Results Compare to Experimental Data?

Parameter

D(A) D(B) D(C)

Experimental ( ppm)

6.22 6.53

5.85

Typical accuracy

Predicted (ppm)

6.44

6.44 5.22 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 Constants Energy level of a nuclei are affected by covalently-bonded neighbors spin-states

1 H 13 C 1 H 1 H

three-bond one-bond

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

+J/4

S J (Hz)

-J/4 a b b a

+J/4

I S

The magnitude of the separation is called of Hz.

coupling constant

(

) and has units

Coupling Constants

1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1

Pascal's triangle

b) 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) bonding electrons convey spin states of bonded nuclei

1) spin states of nuclei are “coupled” 2) 3) alignment of spin states of bonded nuclei affects energy of the ground ( a ) and excited states ( b ) of observed nuclei Coupling pattern and intensity follows Pascal’s triangle b a

Common NMR Splitting Patterns

Multiplets consist of 2nI + 1 lines

I is the nuclear spin quantum number (usually 1/2) and n is the number of neighboring spins.

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

Coupling Rules:

1. equivalent nuclei do not interact 2. coupling constants decreases with separation ( typically # 3 bonds) 3. multiplicity given by number of attached equivalent protons (n+1) 4. multiple spin systems 5.

 multiplicity  (n a +1)(n b +1) Relative peak heights/area follows Pascal’s triangle 6. Coupling constant are independent of applied field strength

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

Karplus Equation – Coupling Constants

J = const. + 10Cos f Relates coupling constant to Torsional angle.

Used to solve Structures!

Nuclear Overhauser Effect (NOE)

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

Important:

effect is time-averaged Gives rise to dipolar relaxation (T 1 cross-relaxation and T 2 ) and specially to Perturb affects 1 H spin population 13 C spin population NOE effect

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.

= (I-I

)/I

where I o is thermal equilibrium intensity

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

irradiate ab

N A

N-

N+

A N

Populations and energy levels of a homonuclear AX system (large chemical shift difference) Observed signals only occur from single-quantum transitions

Nuclear Overhauser Effect (NOE)

Saturated (equal population)

bb ab

N-½

S I

N-½ N+½

d d

S N+½

Populations and energy levels immediately following saturation of the S transitions d

Saturated (equal population)

saturate Observed signals only occur from single-quantum transitions ab

N-½

W 1 A

N-½ W

W 0 W 1 X

N+½

2 W 1 X

N+½

W 1 A

Relaxation back to equilibrium can occur through: Zero-quantum transitions (W 0 ) Single quantum transitions (W 1 ) Double quantum transitions (W 2 ) The observed NOE will depend on the “rate” of these relaxation pathways

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, T 1 correlation time ( t c ) and NOE are related through rotational – rotational correlation is the time it takes a molecule to rotate one radian (360 o /2 p ).

• 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

A W

2   

r r

6 6 ( ( 1 3 t 

w 2

t w ( 1 

3 t  w

c X c

2 ) ) 2 t ( w 12 t 

A X



2 ) ) 2 t 3  t

2 )

2 t

c r

6  12 t

c r

NOE is dependent on the distance (1/r 6 ) separating the two dipole coupled nuclei

Important: the effect is time-averaged!

2D NOESY (Nuclear Overhauser Effect)

Relative magnitude of the cross-peak is related to the distance (1/r 6 ) between the protons (≥ 5Ǻ).

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

NMR Structure Determination

NOE Data Is the Fundamental Piece of Information to Determine

Any

Structure (DNA, RNA, Protein, small molecule)

2D NOESY Spectra at 900 MHz Lysozyme Ribbon Diagram

Continuous 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.

% r number of scans

NMR Data Detection and Processing

NMR Pulse

a) b) In FT-NMR, how are all the individual nuclei excited simultaneously?

RF pulses are typically short-duration ( m secs) 1) produces bandwidth (1/4 t ) centered around single frequency 2) shorter pulse width i.

 broader frequency bandwidth

Heisenberg Uncertainty Principal:

Du.D

t ~ 1/2p

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

* =

t p

Pulse length (time, t p )

FT The Fourier transform indicates the pulse covers a range of frequencies

NMR Pulse

NMR pulse length or Tip angle (t p )

B 1

M o

t

=

* t

* B

M xy

The length of time the B 1 field is on => torque on bulk magnetization (B 1 )

A measured quantity – instrument and sample dependent.

NMR Pulse

Some useful common pulses 90 o pulse Maximizes signal in x,y-plane where NMR signal detected

M o

z y x

/ 2

90 o

y z

M xy

180 o pulse Inverts the spin-population.

No NMR signal detected

M o

z x y

Can generate just about any pulse width desired.

p 180 o

y z

-M o

ii.

Sampling the Audio Signal

a) Collect

Digital

1) ADC data by periodically sampling signal voltage – analog to digital converter b) To correctly represent Cos/Sin wave, need to collect data at least twice as fast as the signal frequency c) If sampling is too slow, get folded or aliased peaks Sample Rate - Correct rate, correct frequency -½ correct rate, ½ correct frequency Folded peaks!

Wrong phase!

The

Nyquist Theorem

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

**SR = 1 / (2 * SW)**

SR – sampling rate

Correct Spectra Spectra with carrier offset resulting in

peak folding

aliasing

Sweep Width

(range of radio-frequencies monitored for nuclei absorptions)

iii.

Quadrature detection

a) Frequency of B1 (carrier) is set to the center of the spectra.

1) 2) Small pulse length to excite the entire spectrum Minimizes folded noise b)

How to differentiate between peaks upfield and downfield from carrier?

1) observed peak frequencies are all relative to the carrier frequency c) 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

carrier

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

same frequency relative to the carrier, but opposite sign.

carrier

Use 90 o

two

detectors out of phase.

Phase of Peaks are different.

PH = 0 F PH = 90 F PH = 0 B F B w

(B1)

F S S

iv.

Window Functions

a) Emphasize the signal and decrease the noise by applying a mathematical b) function to the FID.

NMR signal is decaying by T 2 as the FID is collected.

Good stuff Mostly noise Sensitivity Resolution

F(t) = 1 * e - ( LB * t ) – line broadening

Effectively Line-widths adds LB in Hz to peak

Can either increase S/N or Resolution Not Both!

LB = 5.0 Hz Increase Sensitivity FT LB = -1.0 Hz Increase Resolution FT

NMR data size

a) Analog signal is digitized by periodically monitoring the induced current in the b) c) receiver coil How many data points are collected? What is the time delay between data points

Digital Resolution (DR)

– number of Hz per point in the FID for a given spectral width.

DR = SW / TD

d) e) f)

where:

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

Dwell Time (DW)

– constant time interval between data points.

SW = 1 / (2 * DW)

From Nyquist Theorem,

Sampling Rate (SR)

SR = 1 / (2 * SW)

Dependent Valuables

Total Data Acquisition Time (AQ): AQ = TD * DW= TD/2SWH Should be long enough to allow complete delay of FID Higher Digital Resolution requires longer acquisition times

Dwell time

vi.

Zero Filling

a) Improve digital resolution by adding zero data points at end of FID 8K data 8K zero-fill 8K FID 16K FID No zero-filling 8K zero-filling

vii.

NMR Peak Integration or Peak Area

a) The relative peak intensity or peak area is proportional to the number of protons b) associated with the observed peak.

Means to determine relative concentrations of multiple species present in an NMR sample.

HO-CH

-CH

3 1

Relative peak areas = Number of protons

Integral trace

Exchange Rates and NMR Time Scale

NMR time scale refers to the chemical shift time scale

remember

– frequency units are in Hz (sec -1 )  b) exchange rate (k) time scale c) differences in chemical shifts between species in exchange indicate the exchange rate.

Time Scale

Slow Intermediate Fast Range (Sec 1 )

Chem. Shift (

d) k << d A k = d k >> A d A d B d B d B 0 – 1000

Coupling Const. (J)

k << J A - J B k = J A - J B k >> J A - J B 0 –12

T 2 relaxation

k << 1/ T k = 1/ T 2,A 2,A 1/ T 2,B 1/ T 2,B k >> 1/ T 2,A - 1/ T 2,B 1 - 20 d) For systems in fast exchange, the observed chemical shift is the average of the individual species chemical shifts.

obs =

1 +

2 =1

where: f 1 , f 2 d 1 , d 2 – mole fraction of each species – chemical shift of each species

ii.

Effects of Exchange Rates on NMR data

k = p Dn o 2 /2(h e - h o ) k = p Dn o / 2 1/2 k = p ( Dn o 2 Dn e 2 ) 1/2 /2 1/2 k – exchange rate h – peak-width at half-height n – peak frequency e – with exchange o – no exchange k = p (h e -h o )

MultiDimensional NMR

NMR pulse sequences

a) composed of a series of RF pulses, delays, gradient pulses and phases b) in a 1D NMR experiment, the FID acquisition time is the time domain (t 1 ) 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 ( 2 D, 13 C, 15 N) in addition to 1H, but usually detect 1H) 1D NMR Pulse Sequence

ii.

Creating Multiple Dimensions in NMR

a) collect a series of FIDS incremented by a second time domain (t 1 ) 1) evolution of a second chemical shift or coupling constant occurs during this time period b) the normal acquisition time is t 2 .

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 t 1 delay

ii.

Creating Multiple Dimensions in NMR

d) 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

Collections of FIDs with t 1 modulations Fourier Transform t

obtain series of NMR spectra modulated by t 1 Fourier Transform t

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

axis, each point has characteristics of time domain FID Peaks along diagonal are normal 1D NMR spectra Cross-peaks correlate two diagonal peaks by J-coupling or NOE interactions

iii.

Example: 2D NOESY NMR Spectra

a) diagonal peaks are correlated by through-space dipole-dipole interaction (NOE) b) NOE is a relaxation factor that builds-up during the “mixing-time” ( t m ) c) relative magnitude of the cross-peak is related to the distance (1/r 6 ) between the protons (≥ 5 Å ).

2D NOESY NMR Pulse Sequence

Direct (observed) 1 H chemical evolves during t 2 Diagonal peaks corresponds to 1D NMR spectra Indirect (second) 1 H chemical evolves during t 1 NOE intensity evolves during t m Cross peaks correlate diagonal peaks by J-coupling or NOEs

iv.

3D & 4D NMR Spectra

a) similar to 2D NMR with either three or four time domains.

b) additional dimensions usually correspond to 13 C & 15 N 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.

one

experiment may take 2.5 to 4 days to collect.

1) diminished resolution and sensitivity

Spread peaks out by 15 N chemical shift of amide N attached to NH Further spread peaks out by 13 C chemical shift of C attached to CH

Protein NMR

How do you assign a protein NMR spectra?

A collection of “COSY”-like experiments that sequentially walk down the proteins’ backbone Detect couplings to NH 3D-NMR experiments that Require 13 C and 15 N labeled Protein sample

Protein NMR Assignment strategy

We know the primary sequence of the protein.

Correlation of the C

i and C

i & C

i-1 & C

sequentially i-1 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 Connect the overlapping correlation between NMR experiments

Protein NMR Molecular-weight Problem

Higher molecular-weight –> more atoms –> more NMR resonance overlap More dramatic: NMR spectra deteriorate with increasing molecular-weight.

MW increases -> correlation time increases -> T 2 decreases -> line-width increases

NMR lines broaden to the point of not being detected!

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

Protein NMR How to Solve the Molecular-weight Problem?

1) Deuterium label the protein.

• replace • NMR resonances sharpen • 1

problem:

H with 2 H and remove efficient relaxation paths no hydrogens -> no NOEs -> no structure • actually get exchangeable (NH –NH) noes can augment with specific 1 H labeling 2) TROSY • line-width is field dependent