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3. Nuclear Magnetic Resonance

- NMR results from resonant absorption of

electromagnetic energy by a nucleus (mostly protons)changing its spin orientation

- The resonance frequency depends on the chemical

environment of the nucleus giving a specific fingerprint of particular groups (NMR spectroscopy)

- NMR is nondestructive and contact free

- Modern variants of NMR provide 3 structuralresolution of (not too large) proteins in solution 

- NMR tomography (Magnetic resonance imaging!

MR") is the most advanced and po#erful imaging tool 

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$ome history of NMR

%&' rinciple of solid state NMR

(*loch! urcell)

%&+, Resonance frequency depends

on chemical environment (roctor! u)

%&+3 verhauser effect

1956 /irst NMR spectra of protein

(Ribonuclease)

%&+ /ourier Transform

spectroscopy (0rnst)

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*y no#5 More than %+, protein structures

(M 6 , ,,,)

*T"

*ound #ater 

rotein

dynamics 

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/unctional MR"

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3.% rinciple of Nuclear Magnetic ResonanceMany (but not all) nuclei have a spin

(I). 7uantum mechanically I can

have 2I+1 orientations in ane8ternal magnetic field B.

This spin is associated #ith a

magnetic moment 

g I 5 nucle

ar g-factor 

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$ince biomatter is made of 9!:!N and ! these are

the most relevant nuclei for biological NMR

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Mechanical (classical) model 

*, ;; dditional precession of µ= around B% at frequency

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The magnetic moment orients in a magnetic field *,. ifferent orientations

correspond to different energies 

B0" ? %@A

mI = 1/2

mI = - 1/2

 E 

B0

%

9!%3

:!3%

B0" ? %

mI = 1

- 1

 E 

B0

A9! %'N!

0

B0

" ? 3@A mI = 3/2

- 3/2

 E 

B0

A3Na!

-1/2

1/2

g" ? +.+1

2hen photons

#ith frequency 

ω= are absorbeda transition from

the lo#er to the

upper level

occurs. $electionrule ∆m" ? % 

γ  ? 'A.+4 M9

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*ulB magneti sample contains many nuclei (typically N C %,%4 or higher). "n

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The number of spins in state %!A is

The average magneti

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( )1

t  B

ϑ ϑ γ  

=

Thus a pulse of duration τ ?Aπ@' ω% gives a change in angle ofπ@A E pulse ".e. the magneti

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0 0

0 0

( ) ( )

( ) ( )

dn

W n n W n ndt 

dnW n n W n n

dt 

α β β α α  

β 

α α β β  

= − − −

= − − −

This rela8ation is described by a set of rate equations for the

transitions bet#een the states

2hich yields a simple e8ponential rela8ation of the

magneti

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The amplitudes of M8 and My decay #ith another rela8ation

time TA called spin-spin rela8ation time. This rela8ation

originates from inhomogeneity of *, . "t is described by

another phenomenological equation

y

8

y

8

"mmediately

after π@A pulselater 

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ne can detect the transverse

magneti

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3.A :lassical NMR e8periments

 >bsorption

signal

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9igh frequency NMR

spectrometers require verystrong magnetic fields! #hich are

produced using super-cooled

coils (T ? '.AH! liquid 9e). The

superconducting coils are

surrounded by a giant vessel

containing liquid NA.

600 MHz Proton NMR Spectrometer 

B0

*%

B 9e

NA

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3.3 :hemical shiftThe e8ternal field *, is changed (reduced in amplitude) due to local field -σ*,generated by the diamagnetic currents induced by *, in the electron system near the

nucleus. s is the shielding constant (diamagnetic susceptibility)

The shielding depends on the orientation

of *, #ith respect to the molecules (e.g.

ben

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rigin of chemical shift5 ?

shielding of *,

Jsual measure5 /requency

shift of sample (%) relative tosome reference sample (A)K

unit5 ppm 

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*enll carbons are identical

same chemical shift! one line

+ different types of

:-atoms! + lines 

08amples5  %3: NMR

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%9-NMR of ethyl alcohol! :93:9A9

:93

:9A

9

Three types of protons

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Typical chemical shifts  Reference Tetramethylsilane $i (:93) '9as very narro# line

:hemical shifts are frequently used in chemistry and biology to

determine amount of specific groups in sample (quantitative

spectroscopy)

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3.' ulsed NMR More efficient than classical (frequency or *) scans

$tudy the free induction decay (/")

icB up coil

F"dealG /" ? one precession frequency

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FRealG /" ? several precession frequencies

because of several nuclei #ith different chemical

shifts 3% NMR

/T

$ i h

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$pin echo&, degree flip

0volution ? spreading

(dephasing) in 8!y plane

%1, degree flip ? mirror image relative to 8 Refocusing ? spin echo

t

π/2 π

t% t%

 My - echo after A t%

/" TA

  T%

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$pin-$pin "nteractions

$calar  or J E coupling (through bond)

give rise to rela8ation of the magneti E : E * ). "t is short ranged (ma8. A or 3 bond

lengths)

eg 9A

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L- coupling results in additional splitting of (chemically

shifted) linesThe magnetic dipoles of

the :93 group protons

interact #ith the

aldehyde proton spin and

vice versa. arallel

orientations have higher

energies.

N*5 the spin-spin coupling constant L also depends on the bond angle

- info on conformation 

% NMR f l l

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% NMR of macromolecules >lanine in A,

Tryptophan in A,

L-coupling

L-coupling

structure

=ysossignment of lines oB

 >ssignment too complicated

N*5 0R high field

NMR! in principle could

solve resolution problem

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"nteractions bet#een different spin-states

1m∆ = ±

( ) ( )   ( ) ( ) ( )1 11

2 1 3 1 2 4 1 s I 

dnW n n W n n W n n

dt = ∆ − ∆ + ∆ − ∆ + ∆ − ∆

$election rule

demands

Oives rate equations of the type5

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( ) ( )( )   ( )   ( ) ( )( )1 2 1 22 0 2 0   2 z   I I z z I I z z d I 

W W W W I W W S W W I S  dt 

∆= − + + + ∆ − − ∆ − − ∆

1 3 2 4

1 2 3 4

1 3 2 42

 z 

 z 

 z z 

 I n n n n

S n n n n

 I S n n n n

∆ = ∆ − ∆ + ∆ − ∆

∆ = ∆ − ∆ + ∆ − ∆

∆ = ∆ − ∆ − ∆ + ∆

Oenerali

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The same game can be played for the other

magneti

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rotocol5 TaBe /"Ds at variable values of t%

% (auto) peaBs

:ross peaBs indicating spin-spin coupling

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A :$ spectrum of isoleucine

:ross peaBs give information on

distance along the bond

Through bond interaction

be#teen :α9 and :β9CαH

CβH

CδH3

Cγ H2

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A :$ spectrum of a heptapeptide Tyr-Olu->rg-Oly-

 >sp-$er-ro (ORO$)

i t di l di l i t ti (th h ) t B

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irect dipole-dipole interaction (through space) can taBe up a

change of ∆m ? P@- %! ".e. rela8 the selection rules.

*-field generated by dipole µ

Related to the energy changes of > and * due to the

induced fields at > and *5 - µ >B* and - µ*B > 

$trong dependence on distance bet#een the differentspin sites (r - due to dipole interaction) gives very

sensitive spatial information about distances bet#een

spins do#n to ,.+ nm

2 4

0,23 6, IS 

 IS IS 

V W r r 

γ γ  : :

Transition rates go #ith the

square of the interaction

N t B l th t f th ti ti i

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 z   I    z 

S z  z 

 R   I  I  R   S 

S 

σ σ 

•

•

 − − ∆∆     ÷ =  ÷  ÷ ÷   − −   ∆ ÷      ∆  

No# taBe along the cross terms of the magneti

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$implify by assuming R" ?R$5

( )

( ) ( )( )   ( ) ( )( )

( ) ( )( )   ( ) ( )( )

1 2 1 2

1 2 1 2

1exp exp exp exp

2exp 1

exp exp exp exp2

t t t t   R

 Lt t t t t  

 R

σ λ λ λ λ  

σ λ λ λ λ  

 − + − − − − ÷

= ÷ ÷− − − − + − ÷  

This implies ma8imum mi8ing after a time scale τm

/lip the spins $ at that time to enhance

contrast

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:ombine this (Nuclear verhauser) enhancement #ith the

technique of A spectroscopy gives N0$5

/or macromolecules! there are many interacting spins! thus a

much more complicated set of equations #ould have to be

solved

1 1 1

1

1

 j n

i in

n nj n

 R

 R I I 

σ 

σ σ 

σ 

σ 

σ 

•     ÷= ÷

÷  

∆ ∆Ouur uur

The appearance of correlation peaBs as a function of τmi8 gives

information about the spatial properties (σ) of the atoms

art of A N0$ spectrum of a ORO$

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art of A N0$ spectrum of a ORO$

N0$ correlates all

protons near in real space

even if the are chemicallydistant 

H

H

Typical N0$ signatures

etermination of protein structure from

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etermination of protein structure from

multi-dimensional NMR - data

$tarting structure (from

chemical sequence)

Random folding at start of

simulation

9eating to overcome localenergy barriers

:ooling under distance

constraints from NMR

Repeating for many starting

structures 

/amily of structures

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NMR l ti

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Tyrosine hosphatase 

NMR solution

structures of proteins

3 + MR"

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3.+ MR" 

 >t much reduced spatial resolution! NMR can

also be used as an imaging tool! #here thespatial resolution is obtained by encoding

space by a frequency (i.e. a field gradient)

M tl d i b T l ti l

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Mostly driven by TA rela8ations! apply a

gradient field across the sample! #hich gives

different =armor frequencies for differentpositions (all done at 9 frequencies)

Resonance

condition only

fulfilled at one

specific position

N h t l d iti i th

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No# #e have to also encode position in the

8-y direction

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/inally apply a field gradient along the 8

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/inally apply a field gradient along the 8-

direction during readout! #hich gives a

frequency shift of the /" precession

Then you taBe a signal #ith a picBup coil as

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Then you taBe a signal #ith a picBup coil as

a function of /" time and time duration of

the phase coding pulse! #hich you /ourier

transform to obtain a proper image

$ince you have turned a spatial

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$ince you have turned a spatial

measurement into a spectroscopic one! the

resolution is spectroscopically limited (or

limited by the gradients you apply)

Therefore fast scans (needed for functional

studies have less resolution)

Recap $ec 3

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NMR is a spectroscopic method given by

the absorption of em radiation by nuclei

The signals depend on the nuclei! the

applied field and the chemical environment

Jsing /ourier-transform methods! a fast

characteri

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More recap

ipole-ipole interactions can be used to

characteri