biochemistry 530 nmr theory and...

Biochemistry 530

NMR Theory and Practice

Gabriele Varani

Department of Biochemistry

and

Department of Chemistry

University of Washington

1D spectra contain structural information .. but is hard to

extract: need multidimensional NMR

1D spectrum

Dispersed amides:

protein is folded

Ha: protein contains b-sheet

Downfield CH3:

Protein is folded

1D vs 2D homonuclear NMR Spectroscopy

preparation

1D NMR

detection

t

FID

Basic structure of 1D

experiment

preparation evolution detection

t1

2D NMR

m

mixing

t2

Basic structure of 2D

experiment (e.g.

NOESY)

Jeener and Ernst, 1972

2D homonuclear NMR Spectroscopy


t1

2D NMR

m

mixing

t2 Basic

structure

90 90

COSY t1

t1 m

90 90 90

NOESY FID

Two basic

experiments:

NOESY and

COSY

How to generate a 2D experiment: NOESY

1. Record numerous 1D experiments by

systematically incrementing time t1 from 0 to

tmax; the experiment generates a matrix of

points S(t1,t2) which encodes the frequency

information with respect to both t1 and t2

Typical

number of

repetitions (t1

increments)

for

homonuclear

NMR: 256-512

How to process the data to obtain a 2D spectrum

2. Execute the FT for each experiment (each t1 value) with

respect to time t2 to generate an interferogram S(t1, w2)

3. Execute the FT with respect to t1 (for each w2 value) to

generate the final 2D spectrum S(w1,w2)

1D vs 2D NMR spectra of a protein

1D spectrum

amides Ha Side chain CH2

Side chain CH3

NH2

1D vs 2D NMR spectra of a protein

2D projection

representation

2D contour

representation

“cross-peaks” in multidimensional NMR carry structural

information

2D contour

representation:

peaks outside

diagonal are called

cross-peaks

Diagonal is closely

related to 1D

spectrum

Nuclear Overhauser Effect SpectroscopY (NOESY)

The NOESY experiments detects interactions between

spins that are close in space and dipolar coupled: the

magnetization transfer mechanism is essentially the

same as FRET in optical spectroscopy (fluorescence)


t1

2D NMR

m

mixing

t2

x

y

zB

t1 free

precession

Iy

Sy

x

zA

SzIz

90x

90x

x

y

x

zD

mixingm

Iz cos I t1

Sz cos S t1

SI

Sy cos S t1

SI

C z

x

yIx sin I t1Sx sin S t1

Iy cos I t1

zF

x

yI

S

Sy (aSS cos S t1 + aIS cosI t1)Iy (aII cos I t1 + aSI cosS t1)

90x

x

zE

y

SI

Iz cos I t1

Sz cos S t1

(mixing)

consider a two spin system, I & S:

B

90x 90x90x

t2

A

t1

mixing

m

acquireC D FE

1. Excite with 90o

pulse

2. During t1, spins are

labeled with their

Larmor frequency

3. The second 90o

pulse exchanges

rotates magnetization

to -z

5. The final 90o pulse

makes the signal

observable and signal

is acquired in t2

Nuclear Overhause Effect SpectroscopY (NOESY)

x

y

zB

t1 free

precession

Iy

Sy

x

zA

SzIz

90x

90x

x

y

x

zD

mixingm

Iz cos I t1

Sz cos S t1

SI

Sy cos S t1

SI

C z

x

yIx sin I t1Sx sin S t1

Iy cos I t1

zF

x

yI

S

Sy (aSS cos S t1 + aIS cosI t1)Iy (aII cos I t1 + aSI cosS t1)

90x

x

zE

y

SI

Iz cos I t1

Sz cos S t1

(mixing)


B

90x 90x90x

t2

A

t1

mixing

m

acquireC D FE

4. Magnetization is

exchanged between

spin I and S during

the mixing time

Cross-peaks appear between

spins which are close in space

(<5-6 A) (assignments and

structure)

When magnetization is

exchanged, spin I signal

contains information on spin

S and viceversa (cross-

peaks)


90x free precessiont1

90x acquiret2

90x mixingm

[Iy aII cosI t1 + Sy aSS cosS t1 + Iy aSI cosS t1 + Sy aIS cosI t1]

.[ cos I t2 + cos S t2 ]

I

S

IS

crosspeaks

diagonal peaks

IS

aIS

aSI

aSS

aIII,I)

S,I)

S,S)I,S)

F2

F1

I

I

S

S

The mixing coefficients, aIS =

aSI are proportional to the NOE

between these two nuclei

The NOE is related to the

distance r between the two

spins and the correlation

time tc (the time for

reorientation of the IS vector

in the molecule): structure

and motion



90x acquiret2

90x mixingm

[Iy aII cosI t1 + Sy aSS cosS t1 + Iy aSI cosS t1 + Sy aIS cosI t1]

.[ cos I t2 + cos S t2 ]

I

S

IS

crosspeaks

diagonal peaks

IS

aIS

aSI

aSS

aIII,I)

S,I)

S,S)I,S)

F2

F1

I

I

S

S

NOE r IS-6f (tc) m

A simple example: a small immunogenic peptide

COSY and NOESY connectivities in the polypeptide unit

COSY (broken lines) and NOESY (continuous lines)

Protein chemical structure dictates ‘local’ NOE interactions

Sequential and medium range interactions in polypeptides

Protein secondary structure determines local NOE

interactions

Sequential and

medium range NOE

interactions in

regular turns

Protein 3D structure determines local NOE interactions

Sequential and medium

range NOE interactions in

an a-helix

Protein 3D structure determines NOE interactions

Medium and long range NOE interactions

in a parallel and anti-parallel b-sheets

Patterns of NOE interactions define protein secondary

structure

Observable NOE interactions (<5 A) in

regular protein secondary structures

NOE interactions, scalar couplings (and chemical shifts)

can be combined to define protein secondary structure

NOE interactions (<4.5 A) and scalar

coupling patterns in regular protein

secondary structures

A simple example: a small immunogenic peptide

COherence transfer SpectroscopY (COSY)

Cross-section of cross-peak between HN

and Ha proton allows measurement of

scalar couplings for residue C57


The COSY experiments detects interactions

(correlation) between spins that are scalar

coupled: beware, it can only be understood

through quantum mechanics

Sx

Ix sin (I _ JIS)t1++Sx sin (S _ JIS)t1 I

Cz

ySy cos (S _ JIS)t1+

Iy cos (I _ JIS)t1+90x

x

SI

yIx sin (I _ JIS)t1+

+Sx sin (S _ JIS)t1

Dz

t2acquire

B

90x 90x

t2

C DA

t1

acquire


x

zA

90x

x

y

zB

free precessionSzIz

Iy

Sy

t1


t1

2D NMR

m

mixing

t2


1. Excite with 90o pulse

Sx

Ix sin (I _ JIS)t1++Sx sin (S _ JIS)t1 I

Cz

ySy cos (S _ JIS)t1+

Iy cos (I _ JIS)t1+90x

x

SI

yIx sin (I _ JIS)t1+

+Sx sin (S _ JIS)t1

Dz

t2acquire

B

90x 90x

t2

C DA

t1

acquire


x

zA

90x

x

y

zB

free precessionSzIz

Iy

Sy

t1

2. During t1, spins are

labeled with their

Larmor frequency

3. During t1, if spins

are scalar coupled, the

signal encodes this

information as well

4. The second 90o pulse

exchanges

magnetization between

spins: spin I now has

memory of spin S and

viceversa

5. Signal is acquired in t2


Cross-peaks appear between

spins which are scalar

coupled (assignments)


acquiret2

90x

Ix .1/2[sin (I - JIS) t1 - sin (I + JIS) t1]

.1/2[sin (I - JIS) t2 - sin (I + JIS) t2]

Sx .1/2[sin(S - JIS) t1 - sin (S + JIS) t1]

.1/2[sin (S - JIS) t2 - sin (S + JIS) t2]

I

S

IS

crosspeaks

diagonal peaks

ISISJ ISJ

F2

I,S)

I,I)

S,I)

S,S)

S ± JIS/2 I ± JIS/2

I ± JIS/2

S ± JIS/2

F1

The cross-peak fine

structure contains

information on scalar

coupling (structure)

When magnetization is

exchanged, spin I signal

contains information on spin

S and viceversa (cross-

peaks)

Structural information: scalar couplings directly gives

you the torsion angles that define protein or n.a. structure

(Karplus, 1958)

3JHaN=5.9cos2f-1.3cosf +2.2

N

C

Ca

N

C

O

Cb

CaO

HH

H

R

Ca

H

H

f

1

3Jab=9.5cos21-1.6cos1+1.8

Cross-peaks in COSY

experiments occur only

between residues that are

scalar coupled; in turns, these

couplings can be measured in

COSY experiments

COSY and NOESY connectivities in the polypeptide unit

COSY (broken lines) and NOESY (continuous

lines)

Amino acid chemical structure

Different pattern of

scalar couplings

Amino acid identification from scalar coupling patterns

Different pattern

of scalar

couplings allows

amino acid type

identification in

correlated

spectra (COSY,

2QF-COSY,

TOCSY)

This is the first

step towards

complete spectral

assignments of a

protein spectrum

(at least before

heteronuclear

NMR)

Amino acid chemical structure leads to distinct shift for

each residue: random coil chemical shift values

Residue NH aH bH Others

Gly 8.39 3.97

Ala 8.25 4.35 1.39

Val 8.44 4.18 2.13 CH3 0.97, 0.94

Ile 8.19 4.23 1.90 CH2 1.48, 1.19

CH3 0.95

CH3 0.89

Leu 8.42 4.38 1.65,1.65 H 1.64

CH3 0.94, 0.90

Prob 4.44 2.28,2.02 CH2 2.03, 2.03

CH2 3.68, 3.65

NOE interactions, scalar couplings (and chemical shifts)

can be combined to define protein secondary structure

NOE interactions (<4.5 A) and scalar

coupling patterns in regular protein

secondary structures

biochemistry 530 nmr theory and...

Documents